PHYSICS

COACHING NARAYANA PHYSICS (HINGLISH)

SYSTEM OF PARTICLES AND ROTATIONAL

MOTION

Exercise Iv

1. For which of the following does the centre of mass lie

outside the body ?

A. A pencil

B. A shortcut

C. A disc

D. A bangle

Answer: D

Watch Video Solution

2. When a disc rotates with uniform angular velocity,

which of the following is not true ?

A. The sense of rotation remains same

B. The orientation of the axis of rotations remains

same

C. The speed of rotation is non - aero and remains

D. The angular acceleration is non - zero and remains

same

Answer: D

Watch Video Solution

3. In the above problem , the CM of the plate is now in

the following quadrant of x - y plane .

A. I

B. II

C. III

D. IV

Answer: C

View Text Solution

4. The density of a non-uniform rod of length is

given by

where a and b are constants and .

The centre of mass of the rod will be at

A.

B.

C.

1m

ρ(x) = a(1 + bx2)

0 ≤ x ≤ 1

3(a + b)

4(3 + b)

4(a + b)

3(3 + b)

3(a + b)

4(2 + b)

D.

Answer: A

Watch Video Solution

4(3 + b)

3(2 + b)

5. A Merry -go-round, made of a ring-like plarfrom of

radius , is revolving with angular speed

. A person of mass is standing on it. At one instant,

the person jumps o� the round, radially awaay from the

centre of the round (as see from the round). The speed

of the round after wards is

A.

B.

R and massM

ω M

2ω

ω

C.

D.

Answer: B

Watch Video Solution

ω

2

0

6. Choose the correct alternative :

A. For a general rotational motion , angular

momentum L and angular velocity need not be

parallel

B. For a rotational motin about a �xed axis , angular

momentum L and angular velocity are always

ω

ω

parallel

C. For a general translational motion , momentum p

and velocity c are always perpendicular

D. For a general , translational motion ,accelerational

a and velocity v are always parallel .

Answer: A

View Text Solution

7. The net external torque on a system of particles about

an axis is zero. Which of the following are compatible

with it ?

A. The forces may be acting radially from a point on

the axis

B. The forces may be acting on the axis of rotation

C. The forces may be acting parallel to the axis of

rotation

D. All of the above

Answer: D

Watch Video Solution

8. A circular ring of mass 6kg and radius a is placed such

that its center of lies at the origin. Two particles of

masses 2 kg each are placed at the intersecting points

of the circle with positive X-axis and positive Y-axis.

Then, the angle made by the position vector of center of

mass of entire system with X-axis is

A.

B.

C.

D.

Answer: A

Watch Video Solution

45∘

60∘

tan− 1(4/5)

30∘

9. A rod of length 3m and its mass par unit length is

directly proportional to the distance x from its one end .

The centre of gravity of the rod from that end will be at

:-

A. m

B. 2 m

C. m

D. m

Answer: B

Watch Video Solution

1.5

2.5

3.0

10. A wheel is rotating about an axis through its centre

at 720 rpm . It is acted on by a constant torque

opposing its motion for 8 seconds to bring it to rest

�nally . The value of torque ( in N-m ) Is :- (Given

)

A. 48

B. 72

C. 96

D. 120

Answer: B

Watch Video Solution

I = kg − m224π

11. A particle of mass describes a circle of radius .

The centripetal acceleration of the particle is . What

will be the momentum of the particle ?

A. 2m/r

B.

C.

D. 4m/r

Answer: B

Watch Video Solution

m r

4

r2

2m/√r

4m/√r

12. A particle moves in a circular path of radius R with an

angular velocity , where a and b are positive

constants and t is time. The magnitude of the

acceleration of the particle after time is

A. a/R

B.

C.

D.

Answer: D

Watch Video Solution

ω = a − bt

2a

b

a2R

R(a2 + b)

R√a4 + b2

13. A chain couples and rotates two wheels in a bicycle .

The radii of bigger and smaller wheels are 0.5 m and 0.1

m respectively . The bigger wheel rotates at the rate of

200 rotations per minute , then the rate of rotation of

smaller wheel will be :-

A. 1000 rpm

B. 50/3 rpm

C. 200 rpm

D. 40 rpm

Answer: A

Watch Video Solution

14. Five particles of mass 2 kg are attached to the rim of

a circular disc of radius 0.1 m & negligible mass. Moment

of inertia of the system about an axis passing through

the centre of the disc & perpendicular to its plane is

A.

B.

C.

D.

Answer: C

Watch Video Solution

105

104

106

108

15. Four masses are �xed on a mass less rod as shown in

Fig . The moment of inertia about the axis P is about :

` (##NAR_NEET_PHY_XI_P2_C05_E06_024_Q01.png"

width="80%">

A.

B.

C.

D.

Answer: B

View Text Solution

2 kg m2

1 kg m2

0.5 kg m2

0.3 kg m2

16. A rigid body can be hinged about any point on the x-

axis. When it is hinged such that the hinge is at , the

moment of interia is given by

The x-coordinate of centre of mass is.

A. x =2

B. x = 3

C. x = 0

D. x = 1

Answer: B

Watch Video Solution

x

I = 2x2 − 12x + 27

17. Form a circular disc of radius R and mass 9M , a small

disc of mass M and radius R/3 is removed concentrically

. The moment of inertia of the remaining disc about an

axis perpendicular to the the plane of the disc and

passing its centre is :-

A.

B.

C.

D.

Answer: D

Watch Video Solution

MR2

4MR2

MR249

MR2409

18. Two wheels are connected by a belt. The radius of

larger wheel is three times that of the smaller one .

What is the ratio of the rational inertia of larger wheel

to the smaller wheel , when both wheels to the same

angular momentum ?

A. 3

B. 6

C. 9

D. 12

Answer: A

Watch Video Solution

19. A bob of mass m attached to an inextensible string

of length I is suspended from a vertical support. The

bob rotates in a horizontal circle with an angular speed

red/s about the vertical. About the point of

suspension:

A. Angular momentum changes in direction but not

in magnitude

B. Angular momntum changes both in direction and

magnitude

C. Angular momentm is conserved

D. Angular momentum changes in magnitude but

not in direction .

ω

Answer: A

Watch Video Solution

20. At time t = 0 a 2 kg paticle has position vector

relative to the origin Its velocity is

given by (m/s) for t≥0. The torque acting on the

particle about the origin at at t = 2s , is

A. N-m

B.

C. N-m

D. N-m

→r = (4 i − 2j)

v = 2t2

32k

−16kN − m

16k

12k

Answer: A

View Text Solution

21. A solid sphere rolls without slipping and presses a

spring of spring constant as shown in �gure. Then, the

compression in the spring will be

A.

B.

k

√2M

3k

v√2M

5k

C.

D.

Answer: D

Watch Video Solution

v√5M

7k

v√7M

5k

22. The grinding stone of a �our mill is rotating at 600

rad/sec. for this power of 1.2 k watt is used. the e�ective

torque on stone in N–m will be :–

A. 1

B. 2

C. 3

Evaluate Yourself 1

D. 4

Answer: B

Watch Video Solution

1. In a carbon monoxide molecule, the carbon and the

oxygen atoms are separated by a distance

. The distance of the centre of mass from

the carbon atom is

A. Å

B. Å

1.2 × 10− 10m

0.48

0.51

C. Å

D. Å

Answer: C

Watch Video Solution

0.56

0.69

2. Three bodies of equal masses are placed at (0,0) ,(a,0)

and . Find out the cordinates of centre of

mass .

A.

B.

C.

( . )a

2

a√3

2

( , )a

2

a√3

6

(a, )a

2

( , a)√3a

6

D.

Answer: A

Watch Video Solution

( , )a

2a

2

3. If is the position of the centre of mass of a

system of two particles of masses and then

is given by :

A.

B.

C.

D.

→R CM

m1 m2

→R CM

m1 + m2

m1→r 1 + m2

→r 2

m1m2

m1→r 1 + m2

→r 2

m1→r 1 + m2

→r 2

m1 + m2

m1→r 1 + m2

→r 2

m1m2

Answer: C

Watch Video Solution

4. The position of centre of mass of a system consisting

of two particles of masses and seperated by a

distance L apart , from will be :

A.

B.

C.

D.

Answer: B

m1 m2

m1

m1L

m1 + m2

m2L

m2 + m2

Lm2

m1

L

2

Watch Video Solution

5. A string of length is �xed at one end and carries a

mass at the other end. The string makes

revolution per second around the vertical axis through

the �xed end as shown in the �gure, then tension in the

L

M 2/π

string is.

A. Ml

B. 2 Ml

C. 4 Ml

D. 16 Ml

Answer: D

Watch Video Solution

6. A rigid body rotates about a �xed axis with variable

angular velocity equal to (a - bt) at time t where a and b

are constants. The angle through which it rotates

before it comes to rest is

A.

B.

C.

α2

2β

α2 − β2

2α

α2 − β2

2β

D.

Answer: A

Watch Video Solution

α(α − β)

2

7. Two wheels of radii 10 cm and 30 cm are connected to

each other by a belt. What is the ratio of the moment of

inertia of the larger wheel to that of the smaller wheel,

when both of them have the same angular momentum?

A. 3

B. 6

C. 9

D. 12

Answer: A

Watch Video Solution

8. A particle is moving in circular path with constant

acceleration. In time t after the beginning of motion the

direction of net acceleration is at to the radius

vector at that instant. The angular acceleration of the

particle at that time t is

A.

B.

C.

30∘

3

t2

1

t2

√3

t

D.

Answer: C

Watch Video Solution

√3

t2

9. The angular velocity of a rotating disc decreases

linearly with angular displacement from 60 rev/min to

zero during 10 rev . Determine the angular velocity of

the disc 3 sec after it begins to slow down

A. rad/sec

B. rad/sec

C. rad/sec

20π

10

17π10

(7π)3

Evaluate Yourself 2

D. rad/sec

Answer: B

Watch Video Solution

10π

3

1. Three particles of masses 1 kg , 2kg and 3 kg are

subjected to forces

respectively . The magnitude of acceleration of CM of

the system is :

A.

(3 i − 2j + 2k)N, ( − i + 2j − k)N and ( i + j + k)N

ms − 2√11

6

B.

C.

D.

Answer: C

Watch Video Solution

ms − 2√22

6

ms − 2√146

ms − 2√22

6

2. Two bodies of masses 2kg and 4 kg are moving with

velocities 20 m/s and 10m/s towards each other due to

mutual gravitational attraction . What is the velocity of

their centre of mass ?

A. 5.3ms − 1

B.

C. Zero

D.

Answer: C

Watch Video Solution

6.4ms − 1

8.1ms − 1

3. Two particles of masses 2 kg and 4 kg are approaching

each other with acceleration and ,

respectively, on a smooth horizontal surface. Find the

acceleration of center of mass of the system.

A.

1ms− 2 2ms− 2

1ms2

B.

C.

D.

Answer: A

Watch Video Solution

10ms− 2

5ms− 2

15ms− 2

4. The radius of gyration of a body is independent of :

A. Mass of the body

B. Nature of distribution of mass

C. Axis of rotation

D. None of the above

Answer: A

View Text Solution

5. Given the moment of interia of a disc of mass M and

radii R about any of its diameters to be . What is

its moment of interia about an axis normal to the disc

and passing through a point on its edge .

A.

B.

C.

D.

MR2

4

MR23

2

MR2

2

MR2

2MR2

Answer: A

Watch Video Solution

6. Three point masses each of mass m are placed at the

corners of an equilateral triangle of side 'a' . Then the

moment of inertia of this system about an axis passing

along one side of the triangle is

A.

B.

C.

D.

3mb2

mb2

(3/4)mb2

(2/3)mb2

Answer: C

Watch Video Solution

7. What is the moment of inertia of a ring about a

tangent to the circle of the ring ?

A.

B.

C.

D.

Answer: B

Watch Video Solution

MR23

2

MR2

2

MR2

2MR2

8. The moment of interia of a spherical shell about a

tangent is 20 kg . What is the minimum moment of

intertia about any axis ?

A.

B.

C.

D.

Answer: D

Watch Video Solution

m2

12kg − m2

10kg − m2

20kg − m2

8kgm2

9. Consider a uniform square plate of side 'a' and mass

'm'. The moment of inertia of this plate about an axis

perpendicular to its plane and passing through one of

its corners is

A.

B.

C.

D.

Answer: C

Watch Video Solution

ma25

6

ma21

12

ma2712

ma22

3

10. A uniform thin bar of mass and length is

bend to make a regular hexagon. Its moment of inertia

about an axis passing through the centre of mass and

perpendicular to the plane of the hexagon is :

A.

B.

C.

D.

Answer: A

Watch Video Solution

6m 12L

20m L2

30 m L2

m L212

5

6 m L2

Evaluate Yourself 4

1. Two blocks of masses and are placed on a

frictionless surface and connected by a spring. An

external kick gives a velocity of to the heavier

block in the direction of lighter one. The magnitudes of

velocities of two blocks in the centre of mass frame after

the kick are, respectively,

A.

B.

C.

D.

5kg 2kg

14m/s

14ms− 1

7ms− 1

12ms− 1

10ms− 1

Answer: D

Watch Video Solution

2. In the above question velocities of two blocks in the

centre of mass frame just after the kick are respectively

given by :

A. 4 m/s , 10 m/s

B. 10 m/s, 4m/s

C. 4 m/s,-10m/s

D. 10 m/s , -10m/s

Answer: C

View Text Solution

3. A particle performing uniform circular motion gas

angular momentum . If its angular frequency is double

and its kinetic energy halved, then the new angular

momentum is :

A. 2L

B. 4L

C.

D.

Answer: D

Watch Video Solution

L

L

2

L

4

4. A particle of mass m is �red from the origin of the co-

ordinate axes making angle with the horizontal . At

an instant , its position vector is and

velocity is . The angular momentum of the

particle w.r.t the origin at the instant is

A. 7 m

B.

C.

D.

Answer: D

Watch Video Solution

45∘

→r = 3 i + 4j

→v = 4 i − 3j

k

−7mk

25mk

−25mk

5. A particle of mass m is projected with a velocity v

making an angle of with the horizontal. The

magnitude of the angular momentum of the projectile

abut the point of projection when the particle is at its

maximum height h is.

A. 0

B.

C.

D.

Answer: C

Watch Video Solution

45∘

m√2gh3

mv2√2g

mv2√2g

6. To maintain a rotor at a uniform angular speed of

, an engine needs to transmit a torque of 180

Nm. What is the power of the engine required ?

A. kw

B. 36 kw

C. 72 kw

D. 7.2 kW

Answer: B

Watch Video Solution

200rad s − 1

3.6

7. A thin circular ring of mass and radius is rotating

about its axis with a constant angular velocity . Two

objects each of mass are attached gently to the

opposite ends of a diameter of the ring. The ring now

rotates with an angular velocity

A.

B.

C.

D.

Answer: C

Watch Video Solution

m R

ω

M

ω' =

ωM

M + m

ω(M − 2m)

M + 2m

ωM

M + 2m

ω(M + 2m)

M

8. A body of mass 2 kg and radius of gyration 0.5 m is

rotating about an axis. If its angular speed is 2 rad/s,

then the angular momentum of the body will be

A.

B.

C.

D.

Answer: B

Watch Video Solution

0.5

1.0

2.0

1.5

9. A solid cylinder of mass rotates about its axis

with angular speed . The radius of the cylinder is

. What is the kinetic energy associated with the

rotation of the cylinder ? What is the magnitude of

angular momentum of the cylinder about its axis ?

A. 1625 J

B. 2750 J

C. 3125 J

D. 575 J

Answer: C

Watch Video Solution

20kg

100s− 1

0.25m

10. If the radius of earth contracts 1/n of its present day

value, the length of the day will be approximately

A. 48 hrs

B. 24 hrs

C. 12 hrs

D. 6 hrs

Answer: D

Watch Video Solution

11. A particle of mass is rotating in a plane in circular

path of radius . Its angular momentum is . The

m

r L

Evaluate Yourself 3

centripetal force acting on the particle is

A.

B.

C.

D.

Answer: A

Watch Video Solution

L2

m r

L2m

r2

( )2

L2

m r

( )2

L2

m r

1. A cord is wound round the circumference of wheel of

radius . The axis of the wheel is horizontal and �xed

and moment of inertia about it is . A weight is

attached to the end of the cord and falls from rest. After

falling through a distance , the angular velocity of the

wheel will be.

A.

B.

C.

D.

Answer: B

Watch Video Solution

r

I mg

h

√2gh

I + mr

[ ]2mgh

I + mr2

12

[ ]2mgh

I + 2m

12

√2gh

2. A cubical block of mass M and edge a slides down a

rougg inclined plane of inclination with a uniform

velocity. The torque of the normal force on the block

about its centre has magnitude.

A. zero

B. Mga

C. Mga

D.

Answer: D

Watch Video Solution

θ

sin θ

(mga sin θ)

2

3. Find the torque of a force about the

origin. The force acts on a particle whose position

vector is

A.

B.

C.

D.

Answer: A

Watch Video Solution

7 i + 3j − 5k

i − j + k

2 i + 12j + 10k

10 i + 2j + 12k

15 i + 10j + 8k

4 i + 6j + 18k

Evaluate Yourself 5

4. A rope is wound round a hollow cylinder of mass 3 kg

and radius 40 cm. What is the angular acceleration of

the cylinder if the rope is pulled with a force of 30 N.

A.

B.

C.

D.

Answer: C

Watch Video Solution

50s− 2

75s− 2

25s− 2

100s− 2

1. A solid cylinder rolls up an inclined plane of angle of

inclination . At the bottom of the inclined plane, the

centre of mass of the cylinder has a speed of .

(a) How far will the cylinder go up the plane ? (B) How

long will it take to return to the bottom ?

A. m

B. m

C. m

D. m

Answer: A

Watch Video Solution

30∘

5m/s

3.8

2.6

4.2

5.7

2. A ball is thrown down a lawn in such a way that it

initially slides with a speed without rolling. It

gradually picks up rotational motion. Prove that it will

be without sliding, that is, its motion will be pure rolling

when its speed falls to .

A.

B.

C.

D.

Answer: C

Watch Video Solution

v0

v05

7

v02

7

v03

7

v05

7

v075

3. A loop rolls down on an inclined plane. The fraction of

its kinetic energy that is associated with only the

rotational motion is.

A.

B.

C.

D.

Answer: A

Watch Video Solution

1: 2

1: 3

1: 4

2: 3

4. A solid cylinder of mass and radius rolls down

an inclined plane of height without slipping. The

speed of its centre when it reaches the bottom is.

A.

B.

C.

D.

Answer: B

Watch Video Solution

M R

h

√2gh

√ gh43

√ gh3

4

√4g

h

5. A body of mass M and radius R is rolling horizontally

without slipping with speed v . It then rolls up a hill to a

maximum height h . If , what is the M.I of the

body ?

A.

B.

C.

D.

Answer: B

Watch Video Solution

h =5v2

6g

MR2

2

MR22

3

Mr23

4

MR22

5

6. A heavy disc is thrown on a horizontal surface in such

a way that it slides with a speed intially without

rollind . It will start rolling without slipping when its

speed is reduced

A.

B.

C.

D.

Answer: B

Watch Video Solution

V0

V01

3

V02

3

V03

5

V05

7

C U Q

1. The concept of CM is applicable

A. only for rigid bodies

B. only for a system of collection of particles

C. for both , system of collection of particles and

rigid bodies .

D. none of the above ( here , CM = centre of mass )

Answer: C

View Text Solution

2. If ecternal force acting on a system is constant . It

means that the velocity of the CM .

A. is constant

B. is variable

C. depends on internal forces

D. None of the above

Answer: B

View Text Solution

3. The centre of mass of a body

A. lies always at the geometrical centre

B. lies always indlide the body

C. lies always outside the body

D. may lie within or outside the body

Answer: D

Watch Video Solution

4. The centre of mass of a system of particles does not

depend on

A. masses of the particles

B. forces acting on the particles

C. position of the particles

D. relative distances between the particles

Answer: B

View Text Solution

5. The centre of mass of a body

A. depends on the choice of co - ordinate system

B. is independent of the choice of co - ordinate

system .

C. may or may not depend on the choice of co -

ordinate system

D. None of the above

Answer: B

View Text Solution

6. Two bodies initially at rest are attrached

towards each other due to gravitation. Given that is

much heavier than . Which of the followings correctly

describes the relative motion of the centre of mass of

the bodies ?

A. It moves towards A

B. It remains at rest w.r.t A as well as B

C. It moves towards B

A and B

A

B

D. It moves perpendicular to the line joining the

particles

Answer: B

Watch Video Solution

7. A uniform straight rod is placed in vertical position on

a smooth horizontal surface and released. As the rod is

in motion, the centre of mass moves

A. horizontally

B. vertically down

C. in a parabolic path

D. does not move .

Answer: B

Watch Video Solution

8. Centre of mass of the earth-moon system lies

A. on the surface of the earth

B. on the surface of the moon

C. with in the earth

D. at the midpoint of the line joining their centres

Answer: C

W t h Vid S l ti

Watch Video Solution

9. Two balls are thrown simultaneously in air. The

acceleration of the centre of mass of the two balls while

in air

A. depends on masses of the balls

B. depends on the direction of motion of the balls

C. depends on speed of the balls

D. depends on speeds of the balls

Answer: D

Watch Video Solution

10. For a rotating body about �xed axis ,

A. every particle moves in a circle

B. the linearvelocity is related to angular velocity

C. Both (1) and (2) are correct

D. Both (1) and (2) are incorrect

Answer: C

View Text Solution

11. For a pure rotational motion ,

A. is same for all particles of bodyω

B. linear velocity of each particle is same at an

instant of time

C. are constant for all aprticles

D. None of the above

Answer: A

View Text Solution

∨ and ω

12. Choose the correct option for rotational motion .

A. The direction of angular velocity is perppendicular

to the axis of rotation

B. The direction of angular velocity is ablong the axis

of rotation

C. For rotational motion , the angular velocity of

each particle is di�erent

D. None of the above

Answer: B

Watch Video Solution

13. Two particles and located at distances and

respectively from the centre of a rotating disc such that

.

p q rp rq

rp > rq

A. both p and q have the same acceleration

B. both p and q do not have any acceleration

C. both p and q do not have any acceleration

D. p ' has greater acceleration than 'q'

Answer: C

Watch Video Solution

14. Identify the increase in order of the angular

velocities of the following

(A) earth rotating about its own axis

(b) hour's hand of a clock

(c) second's hand of a clock

(d) �ywheel of radius 2 m making 300 rpm

A. earth rotating about its own axis

B. hours hand of a clock

C. seconds hand of a clock

D. �y wheel of radius 2m making 300 rps

Answer: A

Watch Video Solution

15. The direction of following vectors is along the line of

axis of rotation

A. angular velocity , angular acceleration only

B. angular velocity , angular momentum only

C. angar velocity , angular acceleration , angular

momentum only

D. angular velocity , angular acceleration , angular

momentum and torque

Answer: D

Watch Video Solution

16. The correct relation of the following is

A. →τ =→r .

→F

B.

C.

D.

Answer: B

Watch Video Solution

→τ =

→r ×

→F

→τ =

→F→r

→τ =

→r +

→F

17. Which of the following is wrong

A. Direction of torque is parallel to axis of rotation

B. Direction of moment of couple is perpendicular to

the plane of rotation of body

C. Torque vector is perpendicualr to both position

vector and force vector

D. The direction of force vector is always

perpendicular to both the directions of position

vector and torque vector

Answer: D

Watch Video Solution

18. If force vector is along X-axis and radius vector is

along Y-axis then the direction of torque is

A. along + ve Z - axis

B. along - ve Z-axis

C. in X-Y plane making an angle with X - axis

D. in X - Y plane making an angle with X - axis

Answer: B

Watch Video Solution

45∘

135∘

19. During rotation of a body, the position vector is

along X-axis and force vector is along Y-axis, The

direction of torque vector is

A. in the X-Y plane

B. along - ve Z - axis

C. along + ve Z -axis

D. in the X-Z plane

Answer: C

Watch Video Solution

20. If the direction of position vector is towards

south and direciton of force vector is towards east,

then the direction of torque vector is

A. towards north

B. towards west

C. vertically upward

→r

→F

→τ

D. vertically downward

Answer: C

Watch Video Solution

21. A circular disc is rotated along clockwise direction in

horizontal plane. The direction of torque is

A. horizontally right side

B. horizontally left side

C. vertically upwards

D. vertically downwards

Answer: D

Watch Video Solution

22. Magnitude of torque is maximum in the following

case

A. radius vector is perpendicular to force vector

B. radius vector is parallel to force vector

C. Angle between radius vector and force vector is

D. Angle between radius vector and force vector is

Answer: A

h id l i

45∘

60∘

Watch Video Solution

23. A constant resultant torque rotates a wheel about

its own axis. Then true statement of the following is

A. angular velocity of wheel is constant

B. angular acceleration of wheel is constant

C. angular acceleration of wheel gradually increases

D. angular momentum of wheel is constant

Answer: B

Watch Video Solution

24. A wheel is free to rotate about its own axis without

friction. A rope is wound around the wheel. If other end

of rope is pulled with a constant force, then true

statement from the following is

A. constant torque is produced and the wheel is

rotated with constant angular velocity

B. constant torque is produced and the wheel is

rotated with constant angular acceleration

C. variable torque is produced and the wheel is

rotated with variable angular velocity

D. variable torque is produced and the wheel is

rotated with variable angular acceleration

Answer: B

Watch Video Solution

25. Class lever is that in which

A. fulcrum is between the load and e�ort

B. load is between the fulcrum and e�ort

C. e�ort iis between the load and fulcrum

D. fulcrum , load and e�ort at one point

Answer: A

Watch Video Solution

I

26. The example of a couple is

A. to open a lid of bottle by �ngers

B. the couple due to magnetic force of the earth on a

compass needle

C. both (1) and 2) are correct

D. both (1) and (2) are incorrect

Answer: C

View Text Solution

27. The example of lever is

A. see - saw

B. beam of balance

C. both (1) and (2) are correct

D. both (1) and (2) are incorrect

Answer: C

Watch Video Solution

28. Then moment of inertia of a rigid body depends on

(A) mass of body

(B) position of axis of rotation

(C) time period of its rotation

(D) angular velocity of the body

A. mass of body

B. position of axis of rotation

C. time period of its rotation

D. angular velocity of the body

Answer: A

Watch Video Solution

29. Moment of inertia of a body depends upon

A. distribution of mass of body

B. position of axis of rotation

C. temperature of the body

D. all the above

Answer: D

Watch Video Solution

30. A brass disc is rotating about its axis. If temperature

of disc is increased then its

A. radius of gyration increases , but moment of

intertia remains the same

B. moment of inertia increases but radius of

guration remains the same

C. radius of gyration , moment of inertia both remain

the same

D. radius of gyration . Moment of intertia both

increase

Answer: D

Watch Video Solution

31. The radius of gyration of a rotating metallic disc is

independent of the following physical quantity.

A. Position of axis of rotation

B. Mass of disc

C. Radius of disc

D. temperature of disc

Answer: B

Watch Video Solution

32. One solid sphere and another hollow sphere are

of same mass and same outer radii. Their moment of

inertia about their diameters are respectively and

such that.

A.

B.

A B

IA IB

IA = IB

IA > IB

C.

D. where & are their densitites .

Answer: C

Watch Video Solution

IA < IB

=IA

IB

dA

dBdA dB

33. The theorem of perpendicular axes is applicable for

A. only planar bodies

B. only regular shaped bodies

C. only three dimensional bodies

D. None of the above

Answer: A

Watch Video Solution

34. Theorem of parallel axes

A. applicable to body of any angle

B. needs MI about an axis passing through CM and

parallel to the axis passing through CM and

parallel to the axis about which we want to know

the MI of the same body

C. Both (1) and (2) are correct

D. Both (1) and (2) are incorrect

Answer: C

Watch Video Solution

35. A boiled egg and a raw egg of same mass and size

are made to rotate about their own axis. If and are

moments of inertia of boiled egg and raw egg, then

A.

B.

C.

D.

Answer: C

I1 I2

I1 = I2

I1 > I2

I1 < I2

I1 = √2I2

Watch Video Solution

36. Raw and boiled eggs are made to spin on a smooth

table by applying the same torque. The egg that spin

faster is

A. Raw egg

B. Boiled egg

C. Both will have same spin rate

D. Di�cult to predict

Answer: B

Watch Video Solution

37. The radius of gyration of a rotating circular ring is

maximum about following axis of rotation

A. natural axis

B. axis passing through diameter of ring

C. axis passing through tangent of ring n its plane

D. axis passing through tangent of ring

perpendicular to plane of ring .

Answer: D

Watch Video Solution

38. A moment of inertia of a thin circular plate is

minimum about the following axis

A. axis perpendicular to plane of plate passing

through its centre

B. axis passing through any diameter of plate

C. axis passing through any tangent of plate in its

palne

D. axis passing through any tangent perpendicular

to its plane

Answer: B

Watch Video Solution

39. A ring of mass and radius is melted and then

moulded into a sphere. The moment of inertia of the

sphere will be

A. more than of the ring

B. less than that of the ring

C. equal to that of the ring

D. none of the above

Answer: B

Watch Video Solution

m r

40. Identify the correct order in which the ratio of radius

of gyration to radius increases for the following bodies.

(I) rolling solid sphere

(II) rolling solid cylinder

(III) rolling hollow sphere

(IV) rolling hollow cylinder

A. I,II,IV,III

B. I,III,II,IV

C. II,I,IV,III

D. II,I,III,IV

Answer: A

Watch Video Solution

41. Identify the increasing order of radius of gyration of

following bodies of same radius

(I) About natural axis of circular ring

(II) about diameter of circular ring

(III) About diameter of circular plate

(IV) about diameter of solid sphere

A. II,III,IV,I

B. III, II,IV,I

C. III,IV,II,I

D. II,IV,III,I

Answer: C

Watch Video Solution

42. Identify the decreasing order of radius of gyration of

following bodies of same radius

(I) About diameter of circular ring

(II) About diameter of circular plate

(III) About tangent of circular ring to its plane

(IV) About tangent of circular plate in its plane

A. III, IV,II,I

B. IV,III,I,II

C. IV,III,II,I

D. III,IV,I,II

⊥r

Answer: D

Watch Video Solution

43. Three dense point size bodies of same mass are

attached at three vertices of a light equilateral

triangular frame . Identify the increasing order of their

moment of inertia about following axis .

I) About an axis to plane and passing through a

corner

II) About an axis to plane passing through centre

III) About bisector of any side .

A. III,I,II

⊥r

⊥r

⊥r

B. III,I,II

C. III,II,I

D. III,II,I

Answer: A

Watch Video Solution

44. Four point size dense bodies of same mass are

attached at four corners of a light square frame .

Identify the decreasing order of their moments of

inertia about following axes .

I) Passing through any side

II) Passing through opposite corners III) bisector of⊥r

any side

(IV) to the plane and passing through any corner

A. III,IV,I,II

B. IV,III,I,II

C. III,II,IV,I

D. IV,III,II,I

Answer: B

Watch Video Solution

⊥r

45. A circular disc is rotating about its own axis, the

direction of its angular momentum is

A. radial

B. along axis of rotation

C. along tangent

D. perpendicular to the direction of angular velocity

Answer: B

Watch Video Solution

46. Angular momentum of the particle rotating with a

central force is constant due to

A. constant force

B. constant linear momentum

C. zero torque

D. constant torue

Answer: B

Watch Video Solution

47. A solid sphere is rotating in free space. If the radius

of the sphere is increased keeping mass same which one

of the following will not be a�ected?

A. Moment of inertia

B. Angular momentum

C. Angular velocity

D. Rotational kinetic energy

Answer: B

Watch Video Solution

48. The following motion is based on the law of

conservation of angular momentum

(A) rotation of top (B) diving of driver

(C) rotation of ballet dancer on smooth horizontal

surface

(D) a solid sphere that rolls down on an inclined plane

A. A,B and C are true

B. A,B and D are true

C. B,C and D are true

D. A,C and D are true

Answer: A

Watch Video Solution

49. The law of conservation of angular momentum is

obtained from Newton's II law in rotational motion

when

A. external torque is maximum

B. external torque is zero

C. external torque is zero

D. external torque is constant

Answer: C

Watch Video Solution

50. If polar ice caps melt, then the time duration of one

day

A. increases

B. decreases

C. does not change

D. zero

Answer: A

Watch Video Solution

51. If most of the population on earth is migrated to

poles of the earth then the duration of a day

A. increases

B. decreases

C. remains same

D. �rst increases then decreases

Answer: B

Watch Video Solution

52. If earth shrinks then the duration of day

A. increases

B. decreases

C. remains same

D. �rst increases to intial value

Answer: B

Watch Video Solution

53. A ballet dancer is rotating about his own vertical axis

on smooth horizontal �oor. are moment of

inertia, angular velocity, angular momentum, rotational

I, ω, L, E

kinetic energy of ballet dancer respectively. If ballet

dancer stretches himself away from his axis of rotation,

then

A. I increases and , E decrease but L is constant

B. I decreases , and E increase but L is constant

C. I increases , decreases , L and E are constant

D. I increases , increases but L and E are constant

Answer: A

Watch Video Solution

ω

ω

ω

ω

54. A circular wheel is rotating in horizontal plane

without friction about its axis. If a body is gently

attached to the rim of the wheel then following is false.

A. Moment of inertia increases but angular

momentum rmains same

B. Angular velocity decreases but angular

momentum remains same

C. Rotational kinetic energy decreases but angular

momentum ramains same

D. Angular momentum increases but angular velocity

remains same

Answer: D

Watch Video Solution

55. A ballet dancer is rotating at angular velocity on

smooth horizontal �oor. The ballet dancer folds his body

close to his axis of rotation by which his radius of

gyration decreases by of his initial radius of

gyration, his �nal angular velocity is

A.

B.

C.

D.

Answer: D

Watch Video Solution

ω

1/4th

3ω

4

9ω

4

9ω

16

16ω

9

56. If a body is rolling on a surface without slipping such

that its kinetic energy of translation is equal to kinetic

energy of rotation then it is a

A. A ring

B. A disc

C. A spherical shell

D. A sphere

Answer: A

Watch Video Solution

57. If a ring, disc, hollow sphere and solid sphere rolling

horizontally without slipping with the same velocity on

a surface, then translational kinetic energy is more for

A. Ring

B. Disc

C. Sphere

D. We can not say

Answer: D

Watch Video Solution

58. A ring, disc, hollow sphere and solid sphere roll on a

horizontal surface with the same linear speed. If they

have same mass and radius and move without slipping,

rotational kinetic energy is more for

A. Ring

B. Disc

C. Hollow Sphere

D. Solid sphere

Answer: A

Watch Video Solution

59. If is velocity of centre of mass of a rolling body

then velocity of lowest point of that body is

A.

B. vertically down

C. 2V

D. zero

Answer: D

Watch Video Solution

V

√2V

60. If the velocity of centre of mass of a rolling body is

then velocity of highest point of that body is

V

A.

B. V

C. 2V

D.

Answer: C

Watch Video Solution

√2V

V

√2

61. A body is freely rolling down on an inclined plane

whose angle of inclination is . If is acceleration of its

centre of mass then following is correct

A. a = gsin

θ a

θ

B.

C.

D. a = 0

Answer: B

Watch Video Solution

a < g sin θ

a > g sin θ

62. A sphere cannot roll on

A. a smooth horizontal surface

B. a smooth inclined surface

C. a rough horizontal surface

D. a rough inclined surface .

Answer: B

Watch Video Solution

63. When the following bodies of same radius starts

rolling down on same inclined plane, identify the

decreasing order of their times of descent

(I) Solid cylinder , (II) hollow cylinder

(III) hollow sphere ,(IV) solid sphere

A. IV,I,III,II

B. II,III,I,IV

C. I,IV,III,II

D. II,III,IV,I

Answer: B

Watch Video Solution

64. When the following bodies having same radius

starts rolling down on same inclined plane, identify the

increasing order of their accelerations

(I) hollow cylinder ,(II) Solid cylinder

(III) solid sphere, (IV) hollow sphere

A. I,IV,III,II

B. IV,I,II,III

C. I,IV,II,III

D. I,IV,III,II

Answer: C

Watch Video Solution

65. When a ring is rolling and are

velocities of top most point, lowest point, end point of

horizontal diameter, centre of ring respectively, the

decreasing order of these velocities is

A.

B.

C.

D.

V1, V2, V3, V4

V1, V2, V3, V4

V2, V1, V3, V4

V1, V3, V4, V2

V1, V3, V4, V2

Answer: D

Watch Video Solution

66. The increasing order of fraction of total kinetic

energy associated with translatory motion of the

following rolling bodies is

(I) circular ring ,(II) circular plate

(III) solid sphere ,(IV) hollow sphere

A. I,II,IV,III

B. IV,I,II,III

C. I,IV,II,III

D. IV,I,III,II

Answer: C

Watch Video Solution

67. P is a solid sphere and Q is a hollow sphere both

having the same mass and radius .If they roll down from

the top of an inclined plane , on reaching the bottom .

A. Velocity of P is more

B. Velocity of Q is more

C. Velocity of P = velocity of Q

D. None

Answer: A

Watch Video Solution

68. A and B are two identical rings released from the top

of an inclined plane . A slides down and B rolls down.

Then which reaches the bottom �rst ?

A. A

B. B

C. Both in same time

D. None

Answer: A

Watch Video Solution

69. In the above problem , which will reach the bottom

with greater velocity ?

A. A

B. B

C. Both with same velocity

D. None

Answer: A

View Text Solution

70. A ring, a disc a sphere and spherical shells are

simutaneously released to roll down from the top of an

inclined plane of height h. the four bodies will reach the

bottom in the following order

A. Solid sphere , hollow sphere

B. Solid sphere , disc

C. Ring , solid sphere

D. Solid sphere , ring

Answer: D

Watch Video Solution

Exercise I C W

71. In the above question , the reason for the bodies to

have di�erent times of descent is

A. They have same mass

B. They have same radius

C. They have di�erent radii of gyration

D. All

Answer: C

View Text Solution

1. A rigid body consists of a mass located at

and a mass located at

. The position of centre of mass is

A.

B.

C.

D. 0

Answer: B

Watch Video Solution

3kg

→r 1 = (2 i + 5j)m 2kg

→r 2 = (4 i + 2j)m

( j + i)m145

19

5

( i + j)m145

19

5

( i + j)m19

5145

2. Three identical spheres each of mass and radius

are placed touching each other so that their centres

and lie on a straight line. The position of their

centre of mass from centre of is

A.

B. 2R

C.

D.

Answer: B

Watch Video Solution

m R

A, B C

A

2R3

5R3

4R3

3. Two particles of masses 2 kg and 4 kg are approaching

each other with acceleration and ,

respectively, on a smooth horizontal surface. Find the

acceleration of center of mass of the system.

A.

B.

C.

D.

Answer: A

Watch Video Solution

1ms− 2 2ms− 2

1m/s2

2, /s2

3m/s2

4m/s2

4. A boy of mass is standing at one end of a boat

of length and mass . He runs to the other end.

The distance through which the centre of mass of the

boat boy system moves is

A. 0

B. 1 m

C. 2 m

D. 3m

Answer: A

Watch Video Solution

50kg

9m 400kg

5. A dog weighing is standing on a �at boat so that

it is metres from the shore. It walks on the boat

towards the shore and then halts. The boat weighs

and one can assume that there is no friction between it

and water. The dog from the shore at the end of this

time is

A. m

B. m

C. m

D.

Answer: B

Watch Video Solution

5kg

10 4m

20kg

3.4

6.8

12.6

10m

6. Two bodies of di�erent masses and are

moving with velocities and towards each

other due to mutual gravitational attraction. Then the

velocity of the centre of mass is

A.

B.

C.

D. Zero

Answer: D

Watch Video Solution

2kg 4kg

2m/s 10m/s

5ms − 1

6ms − 1

8md− 1

7. If two particles of masses and which are at

rest are separated by a distance of . The two

particles are moving towards each other under a mutual

force of attraction. Then the ratio of distances travelled

by the particles before collision is

A.

B.

C.

D.

Answer: A

Watch Video Solution

3kg 6kg

15m

2: 1

1: 2

1: 3

3: 1

8. Two bodies of and masses have their velocity

and respectively. Then,

the velocity of their centre of mass is

A.

B.

C.

D.

Answer: C

Watch Video Solution

6kg 4kg

5 i − 2j + 10k 10 i − 2j + 5k

5 i + 2j − 8k

7 i + 2j − 8k

7 i − 2j + 8k

5 i − 2j + 8k

9. The angular velocity of a rotating body is

. The linear velocity of the body whose

position vector is

A.

B.

C.

D.

Answer: B

Watch Video Solution

→ω = 4 i + j − 2k

2 i + 3j − 3k

5 i + 8j + 14k

3 i + 8j + 10k

8 i − 3j + 2k

−8 i + 3ˆj + 2k

10. The angle between the vectors and

is

A.

B.

C.

D.

Answer: A

Watch Video Solution

( i + j + k)

( i − j − k)

sin− 1.√8

3

sin− 1( ) +1

3

π

3

cos − 1.√8

3

cos − 1 √8

3

11. The average angular velocity of the seconds hand of a

watch if the seconds hand of the watch completes one

revolution in minute is

A.

B.

C.

D.

Answer: B

Watch Video Solution

1

rads − 1π

15

rads − 1π

30

rads − 1π

45

rads − 1π

7

12. The angular displacement of a particle is given by

then, its angular velocity at

sec is ……

θ = t3 + t2 + t + 1 t = 2

rads− 1

A. 27

B. 17

C. 15

D. 16

Answer: B

Watch Video Solution

13. A body rotating with uniform angular acceleration

covers (radian) in the �rst 5 s after the start. Its

angular speed at the end of 5 s (in rad/s) is

A.

100π

40π

B.

C.

D.

Answer: A

Watch Video Solution

30π

20π

10π

14. A body rotates about a �xed axis with an angular

acceleration of The angle rotated by it during

the time when its angular velocity increases frm 10 rad/s

to 20 rad/s (in radian) is

A. 50

3rad/s2

B. 100

C. 150

D. 200

Answer: A

Watch Video Solution

15. A wheel starts from rest and acquires an angular

velocity of in half a minute . Then its angular

acceleration is

A.

B.

60rad/s

4 rad s− 2

2rad s− 2

C.

D.

Answer: B

Watch Video Solution

1 rad s− 2

0.5 rad s− 2

16. Two particle move in concentio cireles of radii and

such that they maintain a straight line through the

centre. The ratio of their angular veocities is:

A.

B.

C.

r1

r2

r1 : r2

r2 : r1

1: 1

D.

Answer: C

Watch Video Solution

r21 : r2

2

17. A stationary wheel starts rotating about its own axis

at uniform rate amgular acceleration .The time

taken by its to complete rotation is

A. sec

B. 7 sec

C. 11 sec

D. 14 sec

8rad/s2

77

5.5

Answer: C

Watch Video Solution

18. If N and m then torque

is

A.

B.

C.

D.

Answer: D

Watch Video Solution

→F = 2 i − 3j

→r = 3 i + 2j

→τ

12k

13k

−12k

−13k

19. A door 1.6 m wide requires a force of 1 N to be

applied at the free and to open or close it. The force

that is required at a point 0.4 m distant from the hinges

for opening or closing the door is

A. N

B. N

C.

D. 4 N

Answer: D

Watch Video Solution

1.2

3.6

2.4N

20. A weightless rod is acted on by upward parallel

forces of and ends and respectively. The

total leng th of the rod . To keep the rod in

equilibrium a fo rce of should act in the following

manner :

A. downwards at any point between A and B

B. downward at the midpoint of AB

C. downward at a oint C such that AC = 1 m

D. downwards at a point D such that BD = 1 m

Answer: D

Watch Video Solution

2N 4N A B

AB = 3m

6N

21. The mass of a uniform circular ring of radius is

. Calcuate the moment of inertia of the ring about

an axis passing through its centre an perpendicular to

its surface.

A.

B.

C.

D.

Answer: A

Watch Video Solution

0.2m

0.1kg

2 × 10− 3kg m2

3 × 10− 3 kg m2

4 × 10− 3 kg m2

1 × 10− 3 kg m2

22. Two bodies of mass 1 kg and 2 kg are attached to the

ends of a 2 metre long weight less rod . This system is

rotating about an axis passing through middle point of

rod . Calculate M. I of system .

A.

B.

C.

D.

Answer: B

Watch Video Solution

2kg m2

3kg m2

4kg m2

0.5kg m2

23. If the radius of gyration of a solid disc of mass 10 kg

about an axis is 0.40 m, then the moment of inertia of

the disc about that axis is

A.

B.

C.

D.

Answer: A

Watch Video Solution

1.6 kg m2

3.2kg m2

6.4kg m2

9.5 kg m2

24. A hoop of mass & radius is placed on a

nail, then the moment of inertia of the hoop, when it is

rotated about the nail will be ____

A.

B.

C.

D.

Answer: C

Watch Video Solution

500gm 10cm

kgm2

0.005

0.02

0.01

0.03

25. The ratio of moments of inertia of two solid spheres

of same mass but densities in the ratio is

A.

B.

C.

D.

Answer: B

Watch Video Solution

1: 8

1: 4

4: 1

2: 1

8: 1

26. The radius of a solid sphere is and its density .

When it is made to rotate about an axis passing

R D

through any diameter of sphere, expression for its

moment of inertia is

A.

B.

C.

D.

Answer: B

Watch Video Solution

πDR58

7

πDR58

15

πDR528

15

πDR528

5

27. Three particles of masses are at

from the axis of rotation respectively

then the moment of inertia of the system & radius of

1gm, 2gm&3gm

1cm, 2cm&3cm

gyration of the system respectively are …. and …..

A. 63.2.449

B. 60,4.5

C. 36.4.449

D. 36,2.449

Answer: D

Watch Video Solution

gmcm2

cm

28. The radius of gyration of body is when it is

rotating about an axis passing through centre of mass

of body. If radius of gyration of same body is

18cm

30cm

about a parallel axis to �rst axis then, perpendicular

distance between two parallel axes is

A. 12 cm

B. 16 cm

C. 24 cm

D. 36 cm

Answer: C

Watch Video Solution

29. The position of axis of rotation of a body is changed

so that its moment of inertia decreases so that its

moment of inertia decreases by The change

in its radius of gyration is

A. decreases by 18%

B. increases by 18%

C. decreases by 20 %

D. increases by 20 %

Answer: C

Watch Video Solution

36 % . %

30. The diameter of a �y wheel is . Its coe�cient of

linear expansion is . If its temperature is increased by

the percentage increase in its moment of inertia is

R

α

δT

A.

B.

C.

D.

Answer: A

Watch Video Solution

200 × α × ΔT

100 × α × ΔT

50 × α × ΔT

150 × α × ΔT

31. Three point sized bodies each of mass are �xed at

three corners of light triangular frame of side length .

About an axis passing through any side of frame the

moment of inertia of three bodies is

M

L

A.

B.

C.

D.

Answer: A

Watch Video Solution

ML2

3ML2

2

√3ML2

3ML2

32. In above problem about an axis perpendicular to the

palne of frame and passing through a corner of frame

the moment of inertia of three bodies is

A. ML2

B.

C.

D.

Answer: B

View Text Solution

2ML2

√3ML2

3ML2

2

33. In above problem about an axis passing through any

side of frame the moment of inertia of three bodies is

A.

B.

C.

ML2

3ML2

2

3ML2

4

D.

Answer: C

View Text Solution

2ML2

3

34. Four point size bodies each of mass are �xed at

four corners of a light square frame of side length .

The moment of inertia of the four bodies about an axis

perpendicular to the plane of frame and passing

through its centre is

A.

B.

C.

M

L

4ML2

2√2ML2

2ML2

D.

Answer: C

Watch Video Solution

√2ML2

35. The moment of inertia of a metre stick of mass 300

gm , abut an axis at right angles to the stick and located

at 30 cm mark , is

A.

B.

C.

D. none of these

8.3 × 105g − cm2

5.8g − cm2

3.7 × 105g − cm2

Answer: C

Watch Video Solution

36. A torque of 10 Nm is applied on a wheel having

angular momentum of , calculate the angular

momentum of the wheel after 4 seconds.

A.

B.

C.

D.

Answer: A

2kgm2s− 1

42 kg m2s− 1

30kg m2s− 1

80kg m2s− 1

18kg m2s− 1

Watch Video Solution

37. A car of mass 300 kg is travelling on a circular track

of radius 100 m with a constant speed of 60 m/s

Calculate the angular momentum ?

A.

B.

C.

D.

Answer: B

Watch Video Solution

10 × 105 kg mg2s− 1

18 × 105 kg m2s− 1

26 × 105 kg m2s− 1

5 × 105 kg m2s− 1

38. A particle of mass 0.01 kg having position vector

meters is moving with a velocity

m/s . Calculate its angular momentum about the origin.

A. J/sec

B. J/sec

C. J/sec

D. j/sec

Answer: C

Watch Video Solution

→r = (10 i + 6j) 5 i

0.1k

0.3 i

0.3k

0.4k

39. A particle of mass is moving along a circle of

radius with a time period . Its angular momentum is

A.

B.

C.

D.

Answer: C

Watch Video Solution

m

r T

2πmr

T

4πmr

T

2πmr2

T

4πmr2

T

40. A mass is whirled in a circular path with an angular

momentum . If the length of string and angularL

velocity, both are doubled, the new angular momentum

is

A. L

B. 4L

C. 8L

D. 16L

Answer: C

Watch Video Solution

41. The diameter of a disc is . It has a mass of . It

is rotating about its axis with a speed of rotations

in one minute. Its angular momentum in is

1m 20kg

120

kgm2 /s

A.

B.

C.

D. 43

Answer: B

Watch Video Solution

13.4

31.4

41.4

42. A particle performing uniform circular motion gas

angular momentum . If its angular frequency is double

and its kinetic energy halved, then the new angular

momentum is :

L

A. 4L

B. 2L

C. L/2

D. L/4

Answer: D

Watch Video Solution

43. A constant torque acting on a uniform circular wheel

changes its angular momentum from to in .

The torque acted on it is

A.

A 4A 4 sec

3A

4

B.

C.

D.

Answer: A

Watch Video Solution

A

4

2A

4

3A

2

44. If the earth were to suddenly contract to of

its present radius without any change in its mass, the

duration of the new day will be nearly

A. 24/n hours

B. 24 n hours

1/nth

C. hours

D. hours

Answer: C

Watch Video Solution

24/n2

24n2

45. A thin circular ring of mass M and radius r is rotating

about its axis with a constant angular velocity , Two

objects, each of mass m, are attached gently to the

opposite ends of a diameter of the ring. The wheel now

rotates with an angular velocity

A.

B.

ω

ω =

Mω

M + 2m

2mω

M + 2m

C.

D.

Answer: A

Watch Video Solution

mω

M + 2m

2Mω

M + 2m

46. If the radius of earth shrinks by without

change in its mass, the change in its angular velocity

is

A. increase by %

B. increase by %

C. decrease by %

0.2 %

%

0.4

0.1

0.4

D. decrease by %

Answer: A

Watch Video Solution

0.1

47. A metallic circular plate is rotating about its axis

without friction. If the radius of plate expands by

then the change in its moment of inertia is

A. increase by %

B. decrease by %

C. increase by

D. decrease by %

0.1 %

%

0.1

0.1

0.2 %

0.2

Answer: C

Watch Video Solution

48. An automobile engine develops 100H.P. when

rotating at a speed of 1800 rad/min. The torque it

delivers is

A. 350

B. 440

C. 531

D. 628

Answer: B

Watch Video Solution

49. An electric motor exerts a constant torque on

a �y wheel by which it is rotated at the rate of

The power of motor is

A. 110 watt

B. 150 watt

C. 220 watt

D. 300 watt

Answer: B

Watch Video Solution

5Nm

420r ±

50. A circular disc of mass 0.41 kg and radius 10 m rolls

without slipping with a velocity of 2 m/s. The total

kinetic energy of disc is

A. 10 J

B. 6 J

C. 2 J

D. 4 J

Answer: B

Watch Video Solution

51. A metre stick is held vertically with one end on the

�oor and is then allowed to fall . Find the speed of the

other end when it hits the �oor , assuming that the end

of the �oor does not slip . Take g = 10 m/ .

A. 3.2 m/s

B. 5.4 m/s

C. 7.6 m/s

D. 9.2 m/s

Answer: B

Watch Video Solution

s2

[√30m/s]

52. The rotational kinetic energy of two bodies of

moment of inertia and are same . The

ratio of their angular momenta is

A.

B.

C.

D.

Answer: A

Watch Video Solution

9kgm2 1kgm2

3: 1

3: 5

3: 2

1: 3

53. A hollow sphere rolls down a incline of length

without slipping. The speed of centre of mass at the

bottom of plane is

A. 5g/7

B. 5g/14

C. 2g/3

D. g/3

Answer: B

Watch Video Solution

30∘

6m

54. A hollow sphere rolls down a incline of length

without slipping. The speed of centre of mass at the

bottom of plane is

A.

B.

C.

D.

Answer: A

Watch Video Solution

30∘

6m

6ms− 1

3ms− 1

6√2ms− 1

√2ms− 1

55. A ring and a disc of same mass roll without slipping

along a horizontal surface with same velocity. If the

of ring is , then that of disc is

A. 2J

B. 4J

C. 6J

D. 16J

Answer: C

Watch Video Solution

K. E. 8J

56. A solid cylinder of mass M and radius R rolls down an

inclined plane of height h. The angular velocity of the

cylinder when it reaches the bottom of the plane will be

:

A.

B.

C.

D.

Answer: C

Watch Video Solution

√gh1

2R

√gh2

R

√2

R

gh

3

√2

R

gh

2

57. A thin uniform circular ring is rolling down an

inclined plane of inclination without slipping. Its

linear acceleration along the inclined plane will be

A. g

B.

C.

D.

Answer: D

Watch Video Solution

30∘

g

2

g

3

g

4

58. A thin circular ring �rst slips down a smooth incline

then rolls down a rough incline of identical geometry

from same height. Ratio of time taken in the two motion

is :

A.

B. 1

C.

D.

Answer: C

Watch Video Solution

1

2

1

√2

1

4

Exercise I H W

1. Particles of masses and are at

and then

instantaneous position of their centre of mass is

A.

B.

C.

D.

Answer: A

Watch Video Solution

1kg 3kg

2i + 5j + 13k)m ( − 6i + 4j − 2k)m

( − 16i + 17j + 7k)m1

4

( − 8i + 17j + 7k)m1

4

( − 6i + 17j + 7k)m1

4

( − 6i + 17j + 5k)m1

4

2. A particle of mass is thrown horizontally from the

top of a tower and anoher particle of mass is

thrown vertically upward. The acceleration of centre of

mass is

A. g

B.

C.

D.

Answer: A

Watch Video Solution

m

2m

9g

3

2g

3

g

2

3. Two blocks of masses 5kg and 2kg are connected by a

spring of negligible mass and placed on a frictionless

horizontal surface. An impulse provides a velocity of

7m/s to the heavier block in the direction of the lighter

block. The velocity of the centre of mass is :-

A. 4 m/s

B. 5 m/s

C. 2 m/s

D. 3 m/s

Answer: B

Watch Video Solution

4. Two paricle A and B initially at rest, move towards

each other under mutual force of attraction. At the

instant when the speed of A is V and the speed of B is

2V, the speed of the centre of mass of the system is

A. v

B. 2v

C. 3v

D. Zero

Answer: D

Watch Video Solution

5. A man of mass moves on a plank of mass with a

constant velocity with respect to the plank, as shown

in �gure.

a.If the plank rests on smooth horizontal surface,

determine the velocity of the plank.

b If the man travels a distance with respect to the

plank, �nd the distance travelled by the plank with

respect to the ground.

A.

B.

m M

u

L

Mv

m + M

mv

M

C.

D.

Answer: D

Watch Video Solution

Mv

m

mv

m + M

6. Two bodies of masses and are moving

towards each other with and

respectively. Then velocity of centre of mass is

A.

B.

C.

5kg 3kg

2ms− 1 4ms− 1

0.25ms− 1towards 3kg

0.5ms− 1towards5kg

0.25ms− 1towards 5kg

D.

Answer: C

Watch Video Solution

0.5ms− 1towards 3kg

7. Two particles of masses and are separated by

a distance of and are moving towards each other

under mutual force of attraction, the position of the

point where they meet is

A. 12m from 4kg body

B. 12m from 6kg body

C. 8m from 4kg body

4kg 6kg

20cm

D. 10 m from 4 kg body

Answer: A

Watch Video Solution

8. Two objects of masses and have velocities

of and respectively. The velocity

of their centre of mass is

A.

B.

C.

D.

200g 500g

10im/s (3i + 5j)m/s

5i − 25j

i − 25j5

7

5i + j25

7

25i − j5

7

Answer: C

Watch Video Solution

9. The unit vector perpendicular to

and is

A.

B.

C.

D.

Answer: A

Watch Video Solution

→A = 2 i + 3j + k

→B = i − j + k

4 i − j − 5k

√42

4 i − j + 5k

√42

4 i + j + 5k

√424 i + j − 5k

√42

10. If and and is

the angle between the two vectors, then is equal

to

A.

B.

C.

D.

Answer: C

Watch Video Solution

→A = 3i + j + 2k

→B = 2i − 2j + 4k θ

sin θ

2

3

2

√3

2

√72

√13

11. The angular velocity of the seconds hand in a watch

is

A. rad/s

B. rad/s

C. rad/s

D. rad/s

Answer: C

Watch Video Solution

0.053

0.210

0.105

0.42

12. The angular displacement of a particle is given by

, where is time in seconds. Its angularθ = t3 + 2t + 1 t

acceleration at is

A. 14 rad

B. 17 rad

C. 12 rad

D. 9 rad

Answer: C

Watch Video Solution

t = 2s

s− 2

s− 2

s− 2

s− 2

13. A particle is moving with uniform speed

along a circle of radius then the angular velocity of

particle is (in )

0.5m/s

1m

rads− 1

A. 2

B.

C. 1

D.

Answer: D

Watch Video Solution

1.5

0.5

14. A wheel is making revolutions about its ais with

unifrom angular acceleration. Starting from rest, ilt

reaches 100 rev/sec in 4 seconds. Find the angular

acceleration. Find the angle rotated during these four

seconds.

A.

B.

C.

D.

Answer: D

Watch Video Solution

100π

200π

300π

400π

15. The shaft of a motor car rotates at constant angular

frequancy of 3000 revolutions //min .The angle through

which it has turned in one second in radians is

A. 100π

B.

C.

D.

Answer: A

Watch Video Solution

50π

25π

125π

16. Initial angular velocity of a wheel is .It

rotates with a constant angular acceleration of

.Its angular displacement in 2 s is

A. 4 rad

B. 7 rad

2rad/s

3.5rad/s2

C. 8 rad

D. 11 rad

Answer: D

Watch Video Solution

17. A stationary wheel starts rotating about its own axis

at constant angular acceleration. If the wheel completes

rotations in �rst seconds, then the number of

rotations mades by it in next two seconds is

A. 75

B. 100

50 2

C. 125

D. 150

Answer: D

Watch Video Solution

18. A disc of radius 0.1 m starts from rest with an angular

acceleration of .Then linear velocity of the

point on its after 5 s is

A.

B.

C.

4.4rad/s2

0.22ms− 1

2.2ms− 1

4.4ms− 1

D.

Answer: B

Watch Video Solution

1.1ms− 1

19. Show that is equal in magnitude to

the volume of the parallelopiped formed on the three

vectiors, .

A.

B.

C.

D.

→a . (

→b ×

→c )

→a ,

→b and

→c

a. (b × c)

a × (b. c)

a. (b. c)

a × (b × c)

Answer: A

Watch Video Solution

20. A force is applied on a door at point P making an

angle with position vector , by partical observation ,

give the value of theta for which on has to exert

minimum force to rotate the door ?

A.

B.

C.

D.

θ r

00

π

π

2

π

3

Answer: C

Watch Video Solution

21. A meter scale weighs 50 gms and carries 20 gm at

one end , the scale balances when it is suspende at a

distance x cm from other end . Then x I equal to

A. cm

B. cm

C. cm

D. 50 cm

Answer: B

35.7

64.3

14.3

Watch Video Solution

22. A wire of mass and length is bent in the form of

circular ring. The moment of inertia of the ring about its

axis is

A.

B.

C.

D.

Answer: B

Watch Video Solution

m l

ml2

ml2

4π2

ml2

2π2

ml2

2π2

23. The radius of gyration of a body about an axis at a

distance of from its centre of mass is . The

radius of gyration about a parallel axis through centre

of mass is

A. 2 cm

B. 5 cm

C. 4 cm

D. 3 cm

Answer: D

Watch Video Solution

4cm 5cm

24. If moment of inertia of a thin circular plate about

an axis passing through tangent of plate in its plane.

The moment of inertia of same circular plate about an

axis perpendicular to its plane and passing through its

centre is

A.

B.

C.

D.

Answer: B

Watch Video Solution

I

4I5

2I5

4I3

2I3

25. Moment of inertia of a hoop suspended from a peg

about the peg is

A.

B.

C.

D.

Answer: C

Watch Video Solution

MR2

MR2

2

2MR2

3MR2

2

26. The moment of inertia of a solid sphere about an

axis passing through its centre is . The moment0.8kgm2

of inertia of another solid sphere whose mass is same as

mass of �rst sphere, but the density is times density of

�rst sphere, about an axis passing through its centre is

A.

B.

C.

D.

Answer: B

Watch Video Solution

8

0.1kgm2

0.2kgm2

0.4kgm2

0.5kgm2

27. The ratio of moments of inertia of solid sphere about

axes passing through its centre and tangent

respectively is

A.

B.

C.

D.

Answer: B

Watch Video Solution

2: 5

2: 7

5: 2

7: 2

28. Three identical masses, each of mass are placed

at the corners of an equilateral triangle of side . Then

the moment of inertia of this system about an axis

along one side of the triangle is

1kg,

l

A.

B.

C.

D.

Answer: C

Watch Video Solution

3l2

l2

l23

4

l23

2

29. The radius of gyration of a body about an axis at a

distance of from its centre of mass is . The

radius of gyration about a parallel axis through centre

of mass is

4cm 5cm

A. 2 cm

B. 5 cm

C. 4 cm

D. 3 cm

Answer: D

Watch Video Solution

30. The diameter of a �ywheel is increased by 1%

keeping the mass same. Increase in its moment of

inertia about the central axis is

A. 0.02

B. 0.03

C. 0.01

D. %

Answer: A

Watch Video Solution

0.5

31. The variation of moment of inertia I of a solid sphere

of constant mass with radius R is given by

A.

B.

C.

D.

Answer: C

View Text Solution

32. Four particles each of mass are placed at the

corners of a square of side length . The radius of

gyration of the system about an axis perpendicular to

the plane of square and passing through its centre is

A.

B.

C.

m

l

l

√2

l

2

l

D.

Answer: A

Watch Video Solution

√2l

33. In the above problem the moment of inertia of four

bodies about an axis perpendicular to the plane of

frame and passing through a corner is

A.

B.

C.

D.

ML2

2ML2

2√2ML2

4ML2

Answer: D

View Text Solution

34. In the above problem the moment of inertia of four

bodies about an axis perpendicular to the plane of

frame and passing through a corner is

A.

B.

C.

D.

Answer: C

ML2

2ML2

2√2ML2

4ML2

View Text Solution

35. In the above problem the moment of inertia of four

bodies about an axis passing through any side of frame

is

A.

B.

C.

D.

Answer: C

View Text Solution

4ML2

2√2ML2

2ML2

√2ML2

36. Moment of inertia of a solid sphere about its

diameter is . Then moment of inertia about an axis

parallel to its diameter at a distance equal to half of its

radius is

A.

B.

C.

D.

Answer: B

Watch Video Solution

I0

8I0 /13

13I0 /8

7I0 /2

2I0 /7

37. A uniform rod of mass m is bent into the form of a

semicircle of radius R. The moment of inertia of the rod

about an axis passing through A and perpendicular to

the plane of the paper is

A.

B.

C.

D.

ml2

2

2ml2

ml2

π2

2ml2

π2

Answer: D

Watch Video Solution

38. A disc of moment of inertia is acted upon by

a constant torque of 40 Nm. If it is initially at rest, then

the time taken by it to acquire an angular velocity 100

rad/s will be

A. 20 s

B. 10 s

C. 5 s

D. 4 s

2kgm2

Answer: C

Watch Video Solution

39. A circular disc of mass and of radius is

rotating about its natural axis at the rate of .

Its angular momentum is

A.

B.

C.

D.

Answer: B

4kg 10cm

5rad/sec

0.25kgm2s− 1

0.1kgm2s− 1

2.5kgm2s− 1

0.2kgm2s− 1

Watch Video Solution

40. and . The

value of for which the angular momentum is

conserved is

A.

B. 0

C. 1

D. 2

Answer: A

Watch Video Solution

→F = ai + 3j + 6k

→r = 2 i − 6j − 12k

a

−1

41. A particle of mass is rotating in a plane in circular

path of radius . Its angular momentum is . The

centripetal force acting on the particle is

A.

B.

C.

D.

Answer: D

Watch Video Solution

m

r L

L2

mr

L2m

r

L2

mr2

L2

mr3

42. A mass is whirled in a circular path with a constant

angular velocity and its angular momentum is L. If the

string is now halved keeping the angular velocity same,

the angular momentum is

A. L/2

B. L/2

C. L

D. 2L

Answer: A

Watch Video Solution

43. If a uniform solid sphere of diameter 0.2 m and mass

10 kg is rotated about its diameter with an angular

velocity of 2 rad/s, then the its angular momentum in kg

will be

A.

B.

C.

D.

Answer: C

Watch Video Solution

m2 /s

0.01

0.02

0.08

0.04

44. A child is standing with folded hands at the center

of a platform rotating about its central axis. The kinetic

energy of the system is . The child now stretches his

arms so that the moment of inertia of the system

doubles. The kinetic energy of the system now is

A. 2K

B. K/2

C. 4K

D. K/4

Answer: B

Watch Video Solution

K

45. A constant torque acting on a uniform circular disc

changes its angular mkomentum from L to 4L/3 in 2

seconds. Then the magnitude of the torque applied is

A. L/3

B. 2L/3

C. 3L/2

D. L/6

Answer: D

Watch Video Solution

46. If the mass of earth and radius suddenly become

times and of the present value, the length of the

day becomes

A. 24 h

B. 6h

C. 3/2h

D. 3h

Answer: D

Watch Video Solution

2

1/4th

47. A uniform circular disc of radius is rotating about

its own axis with moment of inertia at an angular

velocity if a denser particle of mass is gently

attached to the rim of disc than its angular velocity is

A.

B.

C.

D.

Answer: D

Watch Video Solution

R

I

ω m

ω

Iω(I + mR)

I + mR2

Iω

Iω

I + mR2

48. A ballet dancer spins about a vertical axis at 60 rpm

with his arms closed. Now he stretches his arms such

that M.I. Increases by . The new speed of revolution

is

A. 90 rpm

B. 80 rpm

C. 40 rpm

D. 30 rpm

Answer: C

Watch Video Solution

50 %

49. A metallic circular wheel is rotating about its own

axis without friction. If the radius of wheel expands by

, percentage change in its angular velocity

A. increase b %

B. decreases by %

C. increase by %

D. decrease by %

Answer: D

Watch Video Solution

0.2 %

0.1

0.1

0.4

0.4

50. A wheel at rest has M.I. . It is rotated by a

motor for one minute. The number of rotations

made by the wheel in one minute is

A. 90

B. 450

C. 1800

D. 1200

Answer: C

Watch Video Solution

kgm22

π2

60W

51. The shaft of a motor is making 1260rpm. The torque

supplied by the motor is . The power of motor is

(in )

A. 100

B. 21

C. 13.2

D. 4.8

Answer: C

Watch Video Solution

100Nm

KW

52. A thin ring of mass and radius is rolling at a

speed of . Its kinetic energy is

A. 2J

B. 1 J

C. J

D. Zero

Answer: B

Watch Video Solution

1kg 1m

1ms− 1

0.5

53. A uniform thin rod of length l is suspended from one

of its ends and is rotated at f rotations per second. The

rotational kinetic energy of the rod will be

A.

B.

C.

D.

Answer: C

Watch Video Solution

2mL2π2n2

mL2π2n21

2

mL2π2n22

3

mL2π2n21

6

54. If a sphere of mass and diameter is rolling

at speed of Its rotational kinetic energy is

A. 10J

2kg 10cm

5ms− 1.

B. 30 J

C. 50 J

D. 70 J

Answer: A

Watch Video Solution

55. A solid sphere and a solid cylinder having the same

mass and radius, rolls down the same incline. The ratio

of their acceleration will be

A.

B.

15: 14

14: 15

C.

D.

Answer: B

Watch Video Solution

5: 7

7: 5

56. A solid cylinder of mass and radius rolls down

an inclined plane of height without slipping. The

speed of its centre when it reaches the bottom is.

A.

B.

C.

M R

h

√2gh

√gh

√gh

2

D.

Answer: B

Watch Video Solution

√2gh

3

57. When a solid sphere is rolling along level surface the

percentage of its total kinetic energy that is

translational is

A. 0.29

B. 0.71

C. 0.6

D. 0.4

Answer: B

Watch Video Solution

58. The speed of a uniform solid cylinder after rolling

down an inclined plane of vertical height H, from rest

without sliding is :-

A.

B.

C.

D.

Answer: D

√gH

3

√2gh

3

√gH

√4gh

3

Watch Video Solution

59. A ring is allowed to roll down on an incline of in

without slipping. The acceleration of its centre of mass

is

A.

B.

C.

D.

Answer: D

Watch Video Solution

1 10

9.8ms2

4.9ms− 2

0.98ms− 2

0.49ms− 2

Exercise Ii C W

60. A solid sphere and a spherical shell roll down an

incline from rest from same height. The ratio of times

taken by them is

A.

B.

C.

D.

Answer: A

Watch Video Solution

√21

25

21

25

√25

21

25

21

1. A uniform wire is bent into the form of a rectangle of

length and width . The coordinates of its centre of

mass from a corner are

A.

B.

C.

D.

Answer: D

Watch Video Solution

L W

(0, 0)

( , W)L

2

(L, )W

2

( , )L

2W

2

2. A uniform disc of radius R is put over another unifrom

disc of radius 2R of the same thickness and density. The

peripheries of the two discs touch each other. Locate

the centre of mass of the system.

A. at R/3 from the entre of the bigger disc towards

the centre of the smaller disc .

B. at R/5 from the centre of the bigger disc towards

the centre of the smaller disc

C. at 2R/5 from the centre of the bigger disc towards

the centre of the smller disc

D. at 2R /5 from the centre of the smaller disc

Answer: B

Watch Video Solution

3. If three particles of masses and are

placed at corners of an equilateral triangle of perimeter

then the distance of centre of mass which is at

origin of particles from mass is (approximately)

(Assume on x-axis)

A.

B. m

C.

D.

2kg, 1kg 3kg

6m

1kg

2kg

√6m

√2

m1

√2

2m

Answer: B

Watch Video Solution

4. Six identical particles each of mass are arranged at

the corners of a regular hexagon of side length . If the

mass of one of the particle is doubled, the shift in the

centre of mass is

A. L

B. 6L/7

C. L/7

D.

m

L

L

√3

Answer: C

Watch Video Solution

5. Three particles each of mass are at the corners of

an equilateral triangle of side . If one of the

particles is removed, the shift in the centre of mass is

A. m

B. m

C. m

D. m

Answer: B

2kg

√3m

0.2

0.5

0.4

0.3

Watch Video Solution

6. A bomb of mass at rest at the coordinate origin

explodes into three equal pieces. At a certain instant

one piece is on the x-axis at and another is at

. The position of the third

piece is

A. x = 60 , y = 60 cm

B.

C.

D.

Answer: C

m

x = 40cm

x = 20cm, y = − 60cm

x = − 60cm, y = − 60cm

x = − 60cm, y = 60cm

x = 60cm, y = − 60cm

Watch Video Solution

7. The mass of a uniform ladder of length is . A

person of mass stand on the ladder at a height of

from the bottom. The position of centre of mass of

the ladder and man from the bottom is

A. m

B. m

C. m

D. m

Answer: D

Watch Video Solution

5m 20kg

60kg

2m

1.256

2.532

3.513

2.125

8. Two particles of equal masses have velocities

. First particle hac an

acceleration of the other particle is zero . The centre of

mass of the two particles moves in a path of

A. Straight line

B. Parabola

C. Circle

D. Ellipse

Answer: A

View Text Solution

→v 1 = 4 i and

→v 2 = 4j

9. A body of mass is dropped and another body of

mass is projected vertically up with speed

simultaneously from the top of a tower of height . If

the body reaches the highest piont before the dropped

body reaches the ground, then maximum height raised

by the centre of mass of the system from ground is

A.

B.

C.

D.

Answer: C

Watch Video Solution

m

M u

H

H +u2

2g

u2

2g

H + ( )2

1

2g

Mu

m + M

H + ( )21

2gmu

m + M

10. A rope thrown over a pulley has a ladder with a man

of mass on one of its ends and a counter balancing

mass on its other end. The man climbs with a velocity

relative to ladder. Ignoring the masses of the pulley

and the rope as well as the friction on the pulley axis,

the velocity of the centre of mass of this system is:

A.

B.

C.

D.

Answer: B

m

M

vr

Vrm

M

vrm

2M

vrM

m

vr2Mm

Watch Video Solution

11. The unit vector perpendicular to

and is

A.

B.

C.

D.

Answer: A

Watch Video Solution

→A = 2 i + 3j + k

→B = i − j + k

4 i − j − 5k

√42

4 i − j + 5k

√42

4 i + j + 5k

√424 i + j − 5k

√42

12. An electron is moving with speed along

the positive x-direction in the presence of magnetic

induction . The magnitude of the

force experienced by the electron in

A.

B.

C.

D.

Answer: C

Watch Video Solution

2 × 105m/s

→B = ( i + 4j − 3k)T

N(e = 1.6 × 10− 19C)(→F = q(

→v ×

→B))

18 × 1013

28 × 10− 13

1.6 × 10− 13

73 × 10− 13

13. The linear and angular velocities of a body in

rotatory motion are and respectively. If

the linear acceleration is then its angular

acceleration in is

A. 6

B. 10

C. 12

D. 2

Answer: C

Watch Video Solution

3ms− 1 6rad/s

6m/s2

rads− 2

14. A stationary wheel starts rotating about its own axis

at an angular acceleration . To acquire an

angular velocity 420 revolutions per minute , the

number of rotations made by the wheel is

A. 14

B. 21

C. 28

D. 35

Answer: C

Watch Video Solution

5.5rad/s2

15. A circular disc is rotating about its own axis at a

uniform angular velocity . The disc is subjected to

uniform angular retardation by which its angular

velocity is decreased to during rotations. The

number of rotations further made by it before coming

to rest is

A. 120

B. 60

C. 40

D. 20

Answer: C

Watch Video Solution

ω

ω

2120

16. A wheel starting from rest is uniformly accelerate at

for 10 seconds. It is allowed to rotate uniformly

for the next 10 seconds and is �nally brought to rest in

the next 10 seconds. Find the total angle rotated by the

wheel.

A. 200 rad

B. 400 rad

C. 300 rad

D. 480 rad

Answer: D

Watch Video Solution

4rad

s2

17. A shaft is turning at at time zero.

Thereafter, angular acceleration is given by

Where is the elapsed time

(a). Find its angular speed at s

(b). How much angle does it turn in these ?

A. 25 rad/sec

B. rad/sec

C. 17 rad/sec

D. 22 rad/sec

Answer: B

65rad/s

α = − 10rad/s2 − 5trad/s2

t

t = 3.0

3s

12.5

Watch Video Solution

18. Average torque on a projectile of mass (initial

speed and angle of projection ) between initial and

�nal positions and as shown in �gure, about the

point of projection is :

.

A.

m

u θ

P Q

mu2 sin 2θ2

B.

C.

D.

Answer: A

Watch Video Solution

mu2 cos θ

mu2 sin θ

mu2 cos θ2

19. A metal rod of uniform thickness and of length is

suspended at its division with help of a string. The

rod remains horizontally straight when a block of mass

is suspended to the rod at its division. The

mass of rod is

A. kg

1m

25cm

2kg 10cm

0.4

B. kg

C. kg

D. kg

Answer: C

Watch Video Solution

0.8

1.2

1.6

20. A roller of mass and of radius lying on

horizontal �oor is resting against a step of height .

The minimum horizontal force to be applied on the

roller passing through its centre to turn the roller on to

the step is

A. 980 N

300kg 50cm

20cm

B. 1960 N

C. 2940 N

D. 3920 N

Answer: D

Watch Video Solution

21. Two persons and of same height are carrying a

uniform beam of length . If is at end, the distane

of from the other end so that receive loads in

the ratio is

A. m

P Q

3m Q

P P , Q

5: 3

0.5

B. m

C. m

D. 1 m

Answer: B

Watch Video Solution

0.6

0.75

22. A metallic cube of side length and of mass

metric ton is on horizontal rough �oor. The minimum

horizontal force that should be applied on the cube at a

height from that �oor to turn the cube about its

lower edge is

A. N

1.5m 3.2

1.2m

1.96 × 103

B. N

C. N

D. N

Answer: C

Watch Video Solution

4.9 × 103

1.96 × 104

4.9 × 104

23. A thin rod of mass and length is bent into a

circular ring. The expression for moment of inertia of

ring about an axis passing through its diameter is

A.

B.

M L

ML2

2π2

ML2

4π2

C.

D.

Answer: C

Watch Video Solution

ML2

8π2

ML2

π2

24. Moment of inertia of a thin circular plate of mass ,

radius about an axis passing through its diameter is

. The moment of inertia of a circular ring of mass ,

radius about an axis perpendicular to its plane and

passing through its centre is

A. 2I

B.

M

R I

M

R

I

2

C. 4I

D.

Answer: C

Watch Video Solution

I

4

25. The ratio of radii of two solid spheres of same

material is . The ratio of moments of inertia of

smaller and larger spheres about axes passing through

their centres is

A.

B.

1: 2

1: 4

1: 8

C.

D.

Answer: D

Watch Video Solution

1: 16

1: 32

26. is moment of inertia of a thin circular ring about

an axis perpendicular to the plane of ring and passing

through its centre. The same ring is folded into turns

coil. The moment of inertia of circular coil about an axis

perpendicular to the plane of coil and passing through

its centre is

A. 2I

I

2

B. 4I

C.

D.

Answer: D

Watch Video Solution

I

2

I

4

27. The moment f inertia of a solid cylinder about an axis

parallel to its length and passing through its centre is

equal to its moment of inertia about an axis

perpendicular to the length of cylinder and passing

through its centre . The ratio of radius of cylinder and

its length is

A.

B.

C.

D.

Answer: C

View Text Solution

1: √2

1: 2

1: √3

1, 3

28. The radius of gyration of rod of length and mass

about an axis perpendicular to its length and

passing through a point at a distance from one of

its ends is

L

M

L/3

A.

B.

C.

D.

Answer: C

Watch Video Solution

L√76

L2

9

L

3

L√5

2

29. Three rings each of mass M and radius R are

arranged as shown in the �gure . The moment of inertia

of the system about AB is

`(NAR_NEET_PHY_XI_P2_C07_E11_036_Q01.png"

width="80%">

A.

B.

C.

D.

Answer: D

View Text Solution

3Mr2

MR23

2

5MR2

MR272

30. Two point size bodies of masses are �xed at

two ends of a light rod of length . The moment of

inertia of two bodies about an axis perpendicular to the

length of rod and passing through centre of mass of

two bodies is

2kg, 3kg

1m

A.

B.

C.

D.

Answer: D

Watch Video Solution

0.6kgm2

0.8kgm2

1kgm2

1.2kgm2

31. is moment of inertia of a thin circular plate about

its natural axis. The moment of inertia of a circular ring

whose mass is half of mass of plate but radius is twice

the radius of plate about an axis passing through any

tangent of ring in its plane is

I

A.

B.

C.

D.

Answer: C

Watch Video Solution

3I

4I

6I

1.5I

32. Three indentical thin rods each of mass m and

length L are joined together to form an equilateral

triangular frame . The moment of inertia of frame about

an axis perpendicular to the palne of frame and apssing

through a corner is

A.

B.

C.

D.

Answer: B

Watch Video Solution

2mL2

3

3mL2

2

4mL2

3

3mL2

4

33. Four spheres of diameter 2a and mass M are placed

with their centres on the four corners of a square of

side b. Then moment of inertia of the system about an

axis about one of the sides of the square is :-

A.

B.

C.

D.

Answer: D

Watch Video Solution

Ma2 + 2Mb2

Ma2

Ma2 + 4Mb2

Ma2 + 2Mb28

5

34. The moment of inertia of a hollow sphere of mass

having internal and external radii and about an

axis passing through its centre and perpendicular to its

plane is

Watch Video Solution

M

R 2R

35. Thickness of a wooden circular plate is same as the

thickness of a metal circular plate but density of metal

plate is times density of wooden plate. If moment of

inertia of wooden plate is twice the moment of inertia

of metal plate about their natural axes, then the ratio of

radii of wooden plate to metal plate is

A.

B.

C.

D.

Answer: D

8

1: 2

1: 4

4: 1

2: 1

Watch Video Solution

36. A thin uniform circular disc of mass M and radius R is

rotating in a horizontal plane about an axis

perpendicular to the plane at an angular velocity .

Another disc of mass M / 3 but same radius is placed

gently on the �rst disc coaxially . the angular velocity of

the system now is

A.

B.

C.

D.

ω

4ω2

ω

3ω

4

3ω

8

Answer: C

Watch Video Solution

37. A turn table is rotating in horizontal plane about its

own axis at an angular velocity 90 rpm while a person is

on the turn table at its edge. If he gently walks to the

centre of table by which moment of inertia of system

decreases by , then the time period of rotating of

turn table is

A. sec

B. 1 sec

C. sec

25 %

0.5

1.5

D. 2 sec

Answer: A

Watch Video Solution

38. A uniform cylindrical rod of mass m and length L is

rotating is perpendicular to its axis of symmetry and

passes through one of its edg faces . If the room

temperature increases by 't' and the coe�cient of linear

expansion is , th change in its angular velocity is

A.

B.

C.

α

2αωt

αωt

αωt3

2

D.

Answer: A

View Text Solution

αωt

2

39. A particle of mass is moving alogn the line

with speed . The magnitude of

angular momentum of the particle about the origin is

A. /sec

B.

C. /sec

D. /sec

1kg

y = x + 2 2m/sec

4kg − 0m2

2√2kg −m2

sec

4√2kg − m2

2kg − m2b

Answer: B

Watch Video Solution

40. An energy of is spent in increasing the speed

of a �ywheel from 60 rpm to 360 rpm. Calculate moment

of inertia of �ywheel.

A.

B.

C.

D.

Answer: C

484J

1.6kg m2

0.3 kg m2

0.7 kg m2

1.2 kg m2

Watch Video Solution

41. A constant torque of turns a wheel of

moment of inertia about an axis through

its centre. Its angular velocity after seconds is.

A.

B.

C.

D.

Answer: A

Watch Video Solution

1000N − m

200kg − m2

3

15rad s− 1

22rad s− 1

28 rad s− 1

60 rad s− 1

42. If the angular momentum of a rotating body about

an axis is increased by 10%. Its kinetic energy increases

by

A. 0.2

B. 0.21

C. 0.1

D. -0.21

Answer: B

Watch Video Solution

43. The angular frequency of a fan of moment of inertia

is increased from 30rpm to 60rpm when a

torque of acts on it. The number of revolutions

made by the fan while the angular frequency is

increased from 30rpm to 60rpm

A. rev

B. rev

C. rev

D. rev

Answer: A

Watch Video Solution

0.1kgm2

0.03Nm

7.855

6.855

5.855

8.855

44. A sphere of mass and radius rolls on a

horizontal plane without slipping with a speed . Now it

rolls up vertically, then maximum height it would be

attain will be

A.

B.

C.

D.

Answer: C

Watch Video Solution

m r

u

3u2

4g

5u2

2g

7u2

10g

u2

2g

45. A circular ring starts rolling down on an inclined

plane from its top. Let be velocity of its centre of mass

on reaching the bottom of inclined plane. If a block

starts sliding down on an identical inclined plane but

smooth, from its top, then the velocity of block on

reaching the bottom of inclined plane is

A.

B.

C.

D.

Answer: D

Watch Video Solution

v

v

2

2v

v

√2

√2v

46. A thin rod of length is vertically straight on

horizontal �oor. This rod falls freely to one side without

slipping of its bottom. The linear velocity of centre of

rod when its top end touches �oor is

A.

B.

C.

D.

Answer: D

Watch Video Solution

L

√2gL

√3gL

2

√3gL

√3gL

4

47. A solid cylinder of mass rolls without slipping

down an inclined plane making an angle with the

horizontal. The frictional force between the cylinder and

the incline is

A.

B.

C.

D.

Answer: B

Watch Video Solution

m

θ

mg sin θ

mg sin θ

3

mg cos θ

2mg sin θ

3

48. A metal disc of radius and mass freely rolls

down from the top of an inclined plane of height

without slipping. The speed of its centre of mass on

reaching the bottom of the inclined plane is

A.

B.

C.

D.

Answer: A

Watch Video Solution

R M

h

√4gh

3

√3gh

4

√gh

√gh

2

49. A hollow sphere rolls on a horozontal surface

without slipping. Then percentages of rotational kinetic

energy in total energy is

A. 40 % , 60 %

B. 60 % , 40 %

C. 28 % ,72 %

D. 72 % , 28 %

Answer: A

Watch Video Solution

50. A disc is rolling the velocity of its centre of mass is

then which one will be correct : -

A. The velocity of highest point is and point of

contact is zero

B. The velocity of highest point is and point of

contact is

C. The velocity of highest point is and point of

contact is

D. The velocity of highest point is and point of

contact is

Answer: A

Vcm

2Vcm

Vcm

Vcm

2Vcm

Vcm

2Vcm

2Vcm

Exercise Ii H W

Watch Video Solution

1. Three identical particles each of mass are

arranged at three corners of a square of side . The

distance of the centre of mass from the fourth corners

is

A. 2/3m

B. 4/3m

C. 1m

D. 8/3m

0.1kg

√2m

Answer: B

Watch Video Solution

2. Six identical particles each of mass are arranged at

the corners of a regular hexagon of side length . If the

mass of one of the particle is doubled, the shift in the

centre of mass is

A.

B.

C.

D.

m

L

L

8

√3L

8

3L16

3L4

Answer: B

Watch Video Solution

3. Three particles each of mass are arranged at the

corners of an equililateral triangle of side . If one of

masses is doubled. The shift in the centre of mass of the

system

A.

B.

C.

D.

m

L

l

√3

L

4√3

√3L

4

L

2√3

Answer: B

Watch Video Solution

4. A bomb of mass at rest at the coordinate origin

explodes into three equal pieces. At a certain instant

one piece is on the x-axis at and another is at

. The position of the third piece is

A.

B.

C.

D.

m

x = 60cm

x = 40cm, y = 60cm

x = − 100cm, y = − 60cm

x = − 60cm, y = − 60cm

x = − 60cm, y = 60cm

x = 60cm, y = − 60cm

Answer: A

Watch Video Solution

5. A ceiling fan is rotating about its own axis with

uniform angular velocity . The electric current is

switched o� then due to constant opposing torque is

its angular velocity is reduced to as it completes

rotations. The number of rotations further it makes

before coming to rest is

A. 18

B. 12

C. 9

ω

2ω

330

D. 24

Answer: D

Watch Video Solution

6. A uniform thin rod of length 1m and mass 3 kg is

attached to a uniform thin circular disc ois

A. m

B. m

C. m

D. m

Answer: A

0.375

0.25

0.125

0.475

View Text Solution

7. Two particles of masses and are separated

by a distance . The shift in the centre of mass when the

two particles are interchanged is

A.

B.

C.

D.

Answer: B

Watch Video Solution

p q(p > q)

d

d(p + q) /(p − q)

d(p − q) /(p + q)

dp/(p − q)

dq/(p − q)

8. A circular disc of radius R is removed from a bigger

circular disc of radius 2R such that the circumference of

the discs coincoid . The centre of mass of the new disc is

from the centre of the bigger disc . the value of is

A.

B.

C.

D.

Answer: A

Watch Video Solution

αR α

1/3

1/2

1/6

1/4

9. Two particles of equal masses have velocities

and . First particle has an

acceleration while the

acceleration of the other particle is zero. The centre of

mass of the two particles moves in a path of

A. staight line

B. parabola

C. circle

D. ellipse

Answer: A

Watch Video Solution

→v 1 = 8 i

→v 2 = 8j

→a 1 = (5 i + 5j)ms− 2

10. Two particles of masses and are projected

horizontally in opposite directions from the top of a

tower of height with velocities and

respectively. The horizontal range of the centre of mass

of two particles is

A. m in the direction of 2 kg

B. m in the direction of 3 kg

C. m in the direction of 2 kg

D. m in the direction of 3 kg

Answer: B

Watch Video Solution

2kg 3kg

39.2m 5m/s 10m/s

8√2

8√2

√8

√8

11. The magnitude of two vectors which can be

represented in the form is . Then the

unit vector that is perpendicular to these two vectors is

A.

B.

C.

D.

Answer: A

Watch Video Solution

i + j + (2x)k √18

− i + j

√2i − j

8√2− i + j

8

− i + j

2√2

12. A proton of velocity enters a �eld of

magnetic induction in the proton in (speci�c charge of

proton )

A.

B.

C.

D.

Answer: B

Watch Video Solution

(3 i + 2j)ms− 1

= 0.96 × 108Ckg− 1 [F = q(→v ×

→B)]

0.96 × 108(6 i + 9j + 4k)

0.96 × 108(6 i − 9j − 4k)

0.96 × 108( i − j − k)

0.6 × 108(5 i − 9j − 4k)

13. A vehicle starts from rest and moves at uniform

acceleration such that its velocity increases by

per every second. If diameter of wheel of that vehicle is

, the angular acceleration of wheel is (in )

A. 5

B. 10

C. 15

D. 20

Answer: B

Watch Video Solution

3ms− 1

60cm rads− 1

14. A circular disc is rotating about its own axis at

constant angular acceleration. If its angular velocity

increases from 210 rpm to 420 rpm during rotations

then the angular acceleration of disc is

A.

B.

C.

D.

Answer: A

Watch Video Solution

21

5.5rad//s2

1rad/s2

16.5rad/s2

22rad/s2

15. A ceiling fan is rotating about its own axis with

uniform angular velocity . The electric current is

switched o� then due to constant opposing torque is

its angular velocity is reduced to as it completes

rotations. The number of rotations further it makes

before coming to rest is

A. 18

B. 12

C. 9

D. 24

Answer: D

Watch Video Solution

ω

2ω

330

16. A particle of mass is projected with an initial

velocity at an angle of projection with the

horizontal. The average torque acting on the projectile

at the time at which it strikes the ground about the

point of projection in newton meter is

A. 25

B. 50

C. 75

D. 100

Answer: B

Watch Video Solution

1kg

10ms− 1 45∘

17. A uniform meter scale of mass is placed on table

such that a part of the scale is beyond the edge. If a

body of mass is hung at the end of the scale

then the minimum length of scale that should lie on the

table so that it does not tilt is

A. 30 cm

B. 80 cm

C. 70 cm

D. 60 cm

Answer: D

Watch Video Solution

1kg

0.25kg

18. A heavy wheel of radius and weight is to

be dragged over a step of height , by a horizontal

force applied at the centre of the wheel. The

minimum value of is

A. 20kgwt

B. 1kgwt

C. kgwt

D. kgwt

Answer: C

Watch Video Solution

20cm 10kg

10cm

F

F

10√3

10√2

19. A wheel has a speed of revolution per minute

and is made to slow down at a rate of . The

number of revolutions it makes before coming to rest is

A. 143

B. 272

C. 314

D. 722

Answer: C

Watch Video Solution

1200

4rad/s2

20. A wheel having radius 10 cm is coupled by a belt to

another wheel of radius 30 cm . 1st wheel increases its

angular speed from rest at a uniform rate of .

The time for 2nd wheel to reach a rotational speed of

100rev/min is ... (assume that the belt does not slip )

A. 20 sec

B. 10 sec

C. sec

D. 15sec

Answer: A

Watch Video Solution

1.5rads − 2

1.5

21. A uniform meter scale of mass is placed on table

such that a part of the scale is beyond the edge. If a

body of mass is hung at the end of the scale

then the minimum length of scale that should lie on the

table so that it does not tilt is

A. 90 cm

B. 80 cm

C. 70 cm

D. 60 cm

Answer: D

Watch Video Solution

1kg

0.25kg

22. If is moment of inertia of a thin rod about an axis

perpendicular to its length and passing through its

centre and is its moment of inertia when it is bent

into a shape of a ring then (Axis passing through its

centre and perpendicular to its plane)

A.

B.

C.

D.

Answer: D

Watch Video Solution

I1

I2

I1 =I2

4π2

I2 =I1

π2

=I2

I1

π2

3

=I2

I1

3

π2

23. The mass of a thin circular plate is and its radius

is . About an axis in the plane of plate at a

perpendicular distance from centre of plate, its

moment of inertia is

A.

B.

C.

D.

Answer: B

Watch Video Solution

M

R

R/2

MR2

4

MR2

2

3MR2

4

3MR2

2

24. Two small spheres of mass and are joined

by a rod of length and of negligible mass. The

of the system about an axis passing through

centre of rod and normal to it is

A.

B.

C.

D.

Answer: B

Watch Video Solution

5kg 15kg

0.5m

M. I.

10kgm2

1.25kgm2

20kgm2

8kgm2

25. Ratio of densities of materials of two circular discs of

same mass and thickness the ratio of their

about natural axes is

A.

B.

C.

D.

Answer: B

Watch Video Solution

5: 6 M. I.

5: 6

6: 5

25: 36

1: 1

26. The moment of inertia of ring about an axis passing

through its diameter is . Then moment of inertia of

that ring about an axis passing through its centre and

perpendicular to its plane is

A. 2I

B. I

C. I/2

D. I/4

Answer: A

Watch Video Solution

I

27. The moment of inertia of a solid cylinder about its

natural axis is . If its moment of inertia about an axis

to natural axis of cylinder and passing through one

end of cylinder is then the ratio of radius of

cylinder and its length is

A.

B.

C.

D.

Answer: A

Watch Video Solution

I

⊥r

19I /6

1: 2

1: 3

1: 4

2: 3

28. A thin rod of mass and length is bent into

regular hexagon. The of the hexagon about a

normal axis to plane and through centre of system is

A.

B.

C.

D.

Answer: C

Watch Video Solution

6m 6L

M. I.

mL2

3mL2

5mL2

11mL2

29. A circular disc of radius and thickness has

moment of inertia about an axis passing through its

centre and perpendicular to its plane. It is melted and

recast into a solid sphere. The of the sphere about

its diameter as axis of rotation is

A. Inside the circular plate

B. 2I/3

C. I/5

D. I/10

Answer: C

Watch Video Solution

R R/6

I

M. I

30. Four thin uniform rods each of length L and mass m

are joined to form a square . The moment of inertia of

square about an axis along its one diagonal is

A.

B.

C.

D.

Answer: B

Watch Video Solution

mL2

6

mL22

3

3mL2

4

4mL2

3

31. Two circular loops and are made of the same

wire and their radii are in the ratio . Their moments

of inertia about the axis passing through the centre and

perpendicular to their planes are in the ratio . The

relation between and is

A. m = n

B.

C.

D.

Answer: C

Watch Video Solution

A B

1: n

1:m

m n

m = n2

m = n3

m = n(4)

32. A circular disc is rotating without friction about its

natural axis with an angular velocity . Another circular

disc of same material and thickness but half the raduis

is gently placed over it coaxially. The angular velocity of

composite disc will be

A.

B.

C.

D.

Answer: D

Watch Video Solution

ω

4ω3

8ω

9

7ω8

16ω

17

33. A ballot dancer is rotating about his own vertical axis

on smooth horizontal �oor with a time period .

The dancer �ods himself close to his axis of rotation due

to which his radius of gyration decreases by , then

his new time period is

A. 0.1 sec

B. 0.25 sec

C. 0.32 sec

D. 0.4 sec

Answer: C

Watch Video Solution

0.5 sec

20 %

34.   A uniform metal rod of length L and mass M is

rotating about an axis passing through one of the ends

and perpendicular to the rod with angular speed

omega. If th temperature increases by , then the

change in its angular velocity is proportional to which of

the following? (Coe�cient of linear expansion of rod = a)

A.

B.

C.

D.

Answer: B

Watch Video Solution

t∘C

√ω

ω

ω2

1

ω

35. A ball of mass 1 kg is projected with a velocity of

m/s from the origin of an xy co ordinate axis

system at an angle with a xis ( horizontal) the

angular momentum [ in SI inits ] of the ball about the

point of projection ater 2 s of projection is [ take

] ( y - axis is taken as vertical

A.

B.

C.

D.

Answer: A

20√2

45∘

g = 10m/s2

−400k

200 i

300j

−350j

View Text Solution

36. When of work is done on a �y wheel its

frequency of rotation increase from to . The

of the wheel about the axis of rotations is nearly

A.

B.

C.

D.

Answer: A

Watch Video Solution

200J

4Hz 9Hz

M. I.

0.12 kg m2

0.2 kg m2

0.22 kg m2

0.3 kg m2

37. A �y wheel of is rotating with

an angular velocity of . The torque required to

bring it to rest in is

A. Nm

B. Nm

C. Nm

D. Nm

Answer: D

Watch Video Solution

M. I. 6 × 10− 2kgm2

20rads− 1

4s

1.6

0.6

0.8

0.3

38. If the kinetic energy of a rotating body about an axis

is decreased by 36%, its angular momentum about that

axis is

A. Increases by 72 %

B. Decreases by 72 %

C. Increases by 20 %

D. Decreases by 20 %

Answer: D

Watch Video Solution

39. The moment of inertia of a wheel of radius is

if a tangential force of applied on the

wheel, its rotational after is

A. 16.2 J

B. 51.2 J

C. 25.6 J

D. 24.8 J

Answer: B

Watch Video Solution

20cm

40kgm2 80N

K. E. 4s

40. An initial momentum is imparted to a homogenous

cylinder, as a results of which it begins to roll without

slipping up an inclined plane at a speed of

the plane make an angle with

the horizontal. What height will be the cylinder rise

to?

A. m

B. m

C. m

D. m

Answer: B

Watch Video Solution

v0 = 4m/sec θ = 30∘

h

(g = 10m/s2)

0.8

1.2

1.0

1.6

41. A solid cylinder starts rolling down on an inclined

plane from its top and is velocity of its centre of mass

on reaching the bottom of inclined plane. If a block

starts sliding down on an identical inclined plane but

smooth, from its top, then the velocity of block on

reaching the bottom of inlined plane is

A.

B.

C.

D. v

Answer: C

V

v

√2

√2v

√3

2

√2

3

Watch Video Solution

42. A thin metal rod of length is vertically straight

on horizontal �oor. This rod is falling freely to a side

without slipping. The angular velocity of rod when its

top end touches the �oor is (nearly)

A.

B.

C.

D.

Answer: A

Watch Video Solution

0.5m

7rads− 1

4.2 rad s − 1

3.5rad s − 1

2.1rad s − 1

43. Show that a cylinder will slip on an inclined plane if

the coe�cient of static friction between the plane and

the cylinder is less than where is the angle of

the inclination with the horizontal.

A.

B.

C.

D.

Answer: A

Watch Video Solution

tan θ1

3θ

tan θ1

3

sin θ1

3

tan θ2

3

sin θ2

3

44. A thin metal disc of radius and mass

starts from rest and rolls down an inclined plane. If its

rotational kinetic energy is at the foot of the inclined

plane, then its linear velocity at the same point is

A. 1 m/s

B. 4m/s

C. 6 m/s

D. 8 m/s

Answer: B

Watch Video Solution

0.25m 2kg

4J

45. A ball rolls without slipping. The radius of gyration

of the ball about about an axis passing through its

center of mass is K. If radius of the ball be R, then the

fraction of total energy associated with its rotational

energy be

A.

B.

C.

D.

Answer: C

Watch Video Solution

K2 + R2

R2

K2

R2

K2

K2 + R2

R2

K2 + R2

46. A wheel is rolling uniformly along a level road

without slipping . Velocity of the highest point on its rim

about the road is V . Then magnitude of velocity of a

point on its rim which is at the same level as that of the

centre is

A.

B.

C. 2V

D.

Answer: D

Watch Video Solution

√2V

V /2

V /√2

Exercise Iii

1. The moment of inertia of a uniform circular disc of

radius and mass about an axis passing from the

edge of the disc and normal to the disc is.

A.

B.

C.

D.

Answer: C

Watch Video Solution

R M

MR2

MR22

5

MR23

2

MR21

2

2. A wheel has angular acceleration of and an

initial angular speed of . In a tine of it has

rotated through an angle (in radian) of

A. 6

B. 10

C. 12

D. 4

Answer: B

Watch Video Solution

3.0rad/s2

2.00rad/s 2s

3. The ratio of the radii of gyration of a circular disc to

that of a circular ring, each of same mass and radius,

around their respective axes is.

A.

B.

C.

D.

Answer: B

Watch Video Solution

√3: √2

1: √2

√2: 1

√2: √3

4. A thin rod of length and mass is bent at its

midpoint into two halves so that the angle between

them is . The moment of inertia of the bent rod

about an axis passing through the bending point and

perpendicular to the plane de�ned by the two halves of

the rod is.

A.

B.

C.

D.

Answer: B

Watch Video Solution

L M

90∘

ML2

24

ML2

12

ML2

6

√2ML2

24

5. A thin circular ring of mass and radius is

rotating in a horizontal plane about an axis vertical to

its plane with a constant angular velocity . If two

objects each of mass be attached gently to the

opposite ends of a diameter of the ring, the ring will

then rotate with an angular velocity

A.

B.

C.

D.

Answer: B

M R

ω

m

ω(M − 2m)

M + 2m

ωM

M + 2m

ω(M + 2m)

M

ωM

M + m

Watch Video Solution

6. Two blocks of mass and have position v

ectors and , respectively . The

center of mass of this system has a position vector.

A.

B.

C.

D.

Answer: B

Watch Video Solution

1kg 3kg

i + 2j + k 3 i − 2j + k

−2 i + 2k

−2 i − j + k

2 i − j − 2k

− i + j + k

7. From a circular disc of radius R and 9M , a small disc of

mass M and radius is removed concentrically .The

moment of inertia of the remaining disc about and axis

perpendicular to the plane of the disc and passing

through its centre is

A.

B.

C.

D.

Answer: A

Watch Video Solution

R

3

MR240

9

MR2

4MR2

MR24

9

8. A solid cylinder and a hollow cylinder, both of the

same mass and same external diameter are released

from the same height at the same time on an inclined

plane. Both roll down without slipping. Which one will

reach the bottom �rst ?

A. Both together only when angle of inclination of

plane is

B. Both together

C. Hollow cylinder

D. Solid cylinder

Answer: B

Watch Video Solution

45∘

9. (1) Centre of gravity (C.G.) of a body is the point at

which the weight of the body acts,

(2) Centre of mass coincides with the centre of gravity if

the earth is assumed to have in�nitely large radius,

(3) To evaluate the gravitational �eld intensity due to

any body at an external point, the entire mass of the

body can be cosidered to be concentrated at its C.G..,

(4) The radius of gyration of any body rotating about ab

axis is the length of the perpendicular dropped from thr

C.G. the body to the axis. which one of the following

paries of statements is correct ?

A. D and A

B. A and B

C. B and C

D. C and D

Answer: A

Watch Video Solution

10. A thin circular ring of mass M and radius r is rotating

about its axis with a constant angular velocity , Two

objects, each of mass m, are attached gently to the

opposite ends of a diameter of the ring. The wheel now

rotates with an angular velocity

A.

ω

ω =

(M + 2m)ω

2m

B.

C.

D.

Answer: D

Watch Video Solution

2Mω

M + 2m

(M + 2m)ω

M

Mω

M + 2m

11. A circular disc of moment of inertia is rotating in a

horizontal plane about its symmetry axis with a

constant angular velocity . Another disc of moment of

inertia is dropped co-axially onto the rotating disc.

Initially, the second disc has zero angular speed.

Eventually, both the discs rotate with a constant angular

It

ωi

Ib

speed . Calculate the energy lost by the initially

rotating disc due to friction.

A.

B.

C.

D.

Answer: D

Watch Video Solution

ωf

ω2t

1

2

I 2b

It + Ib

ω2i

1

2

I 2t

(It + Ib)

ω2i

1

2Ib − It

(It = Ib)

ω2i

1

2IbIt

(It + Ib)

12. Two particle which are initially at rest move towards

each other under the action of their internal attraction.

If their speeds are and at any instant, then the

speed of centre of mass of the system will be

A. 2v

B. 0

C. v

D. v

Answer: B

Watch Video Solution

v 2v

1.5

13. The instantaneous angular position of a point on a

rotating wheel is given by the equation

The torque on the wheel becomes zero at

A.

B.

C.

D.

Answer: D

Watch Video Solution

θ(t) = 2t3 − 6t2

t = 0.5s

t = 0.25s

t = 2s

t = 1s

14. The moment of inertia of a thin uniform rod of mass

and length about an axis passing through its mid-

point and perpendicular to its length is . Its moment of

M L

I0

inertia about an axis passing through one of its ends

perpendicular to its length is.

A.

B.

C.

D.

Answer: A

Watch Video Solution

I0 + ML2 /4

I0 + 2ML2

I0 + ML2

I0 + ML2

15. A circular platform is mounted on a frictionless

vertical axle. Its radius and its moment of

inertia about the axle is . It is initially at rest. A

R = 2m

200kgm2

man stands on the edge at the platform and

begins to walk along the edge at the speed of

relative to the ground. Time taken by the man to

complete one revolution is :

A. sec

B. sec

C. sec

D. sec

Answer: C

Watch Video Solution

50kg

1ms− 1

π

3π

2

2π

π

2

16. Three masses are placed on the x-axis : at

origin. at and at . The

distance of the centre of mass from the origin is.

A. 40 cm

B. 45 cm

C. 50 cm

D. 30 cm

Answer: A

Watch Video Solution

300g

500g x = 40cm 400g x = 70cm

17. When a mass is rotating in a plane about a �xed

point, its angular momentum is directed along.

A. A line perpendicular to the plane of rotation

B. The line making an angle of to the plane of

rotation

C. The radius

D. The tangent to the orbit

Answer: A

Watch Video Solution

45∘

18. Two persons of masses and respectively

are at the opposite ends of a boat. The length of the

boat is and weights . The man walks up

to the man and sits with him. If the boat is in still

water the centre of mass of the system shifts by.

A. m

B. m

C. Zero

D. m

Answer: C

Watch Video Solution

55kg 65kg

3.0m 100kg 55kg

65kg

3.0

2.3

0.75

19.

A small object of uniform density rolls up a curved

surface with an initial velocity . It reaches up to a

maximum height of with respect to the initial

position. The object is

(a). Ring

(b). solid sphere

(c). hollow sphere

(d). disc

A. Ring

v

3v2

4g

B. Solid sphere

C. Hollow sphere

D. Disc

Answer: D

Watch Video Solution

20. A solid cylinder of mass and radius is free

to rotate about the horizontal axis. A massless string is

wound round the cylinder with one end attached to it

and other end hanging freely. Tension in the string

required to produce an angular acceleration of

revolution is

50kg 0.5m

2

s− 2

A. 25 N

B. 50 N

C. N

D. 157 N

Answer: D

Watch Video Solution

78.5

21. The ratio of the accelerations for a solid sphere

(mass ) rolling down an incline of

angle without slipping, and slipping down the incline

without rolling is

m, and radiusR

θ

A.

B.

C.

D.

Answer: A

Watch Video Solution

5: 7

2: 3

2: 5

7: 5

22. A force is acting at a point

. The value of for which angular

momentum about origin is conserved is.

A.

→F = ∝ i + 3j + 6k

→r = 2 i − 6j − 12k ∝

−1

B. 2

C. Zero

D. 1

Answer: A

Watch Video Solution

23. A rod of weight is supported by two parallel knife

edges and and is in equilibrium in a horizontal

position. The knives are at a distance from each other.

The centre of mass of the rod is at a distance from .

A.

w

A B

d

x A

WX

d

B.

C.

D.

Answer: D

Watch Video Solution

Wd

X

W(d − X)

X

W(d − X)

d

24. From a disc of radius R and mass m, a circular hole of

diamter R, whose rim passes through the centre is cut.

What is the moment of inertia of the remaining part of

the disc about a perpendicular axis, passing through the

centre?

A. 15MR2 /32

B.

C.

D.

Answer: B

Watch Video Solution

13MR2 /32

11MR2 /32

9MR2 /32

25. A uniform circular disc of radius 50 cm at rest is free

to turn about an axis which is perpendicular to its plane

and passes through its centre. It is subjected to a

torque which produces a constant angular acceleration

of 2 rad . Its net acceleration in at the end of

2 s is approximately

s− 1 ms− 2

A.

B.

C.

D.

Answer: A

Watch Video Solution

8.0

7.0

6.0

3.0

26. A disc and a solid sphere of same radius but

di�erent masses roll o� on two inclined planes of the

same altitude and length. Which one of the two objects

gets to the bottom of the plane �rst ?

A. Disc

B. Sphere

C. both reach at the same time

D. Depends on their masses

Answer: B

Watch Video Solution

27. Two rotating bodies and of masses and

with moments of inertia and have equal

kinetic energy of rotation. If and be their angular

momenta respectively, then

A B m 2m

IA IB(IB > IA)

LA LB

A.

B.

C.

D.

Answer: A

Watch Video Solution

LB > LA

LA > LB

LA =LB

2

LA = 2LB

28. A solid sphere of mass and radius is rotating

about its diameter. A solid cylinder of the same mass

and same radius is also rotating about its geometrical

axis with an angular speed twice that of the sphere. The

m R

ratio of their kinetic emergies of rotation

will be.

A.

B.

C.

D.

Answer: D

Watch Video Solution

(Esphere /Ecylinder)

1: 4

3: 1

2: 3

1: 5

29. A light rod of length has two masses and

attached to its two ends. The moment of inertia of the

l m1 m2

Illustration

system about an axis perpendicular to the rod and

passing through the centre of mass is.

A.

B.

C.

D.

Answer: C

Watch Video Solution

(m1 + m2)l2

√m1m2l2

m1m2

m1 + m2

l2m1 + m2

m1m2

1. Two particles of masses 1kg and 2kg are located at

and . Find the position of their centre of

mass.

Watch Video Solution

x = 0 x = 3m

2. When number of particles of masses

are at distances

units respectively

from origin on the X-axis, then �nd the distance of

centre of mass of the system from origin.

Watch Video Solution

' n'

m, 2m, 3m, …. nm

x1 = 1, x2 = 2, x3 = 3…xn = n

3. When number of particles of masses

are at distances

units respectively

from origin on the X-axis, then �nd the distance of

centre of mass of the system from origin.

Watch Video Solution

' n'

m, 2m, 3m, …. nm

x1 = 1, x2 = 4, x3 = 9…xn = n2

4. When number of particles of masses are at

distances ,units

from origin on the X-axis, then �nd the distance of

centre of mass of the system from origin.

Watch Video Solution

' n' m

x1 = a, x2 = ar, x3 = ar2…xn = arn

5. The position vectors of three particles of mass

are

m, m and

m, respectively. Find the

position vector of their center of mass.

Watch Video Solution

m1 = 1kg, m2 = 2kg and m3 = 3kg

r1 = (( i + 4j + k) r2 = (( i + (j + k)

r3 = (2 i − (j − (2k)

6. If the centre of mass of three particles of masses of

is at , then where should a fourth

particle of mass be placed so that the combined

centre of mass may be at

Watch Video Solution

1kg, 2kg, 3kg (2, 2, 2)

4kg

(0, 0, 0).

7. Show that the centre of mass of uniform rod of mass

M and length L lies at the middle point of the rod.

Watch Video Solution

8. Find the centre of mass of a uniform triangula lamina.

Watch Video Solution

9. Find the coordination of the centre of mass of a

uniform semicircular wire of radius R and mass M.

Watch Video Solution

10. If the linear density of a rod of length L varies as

, �nd the position of its centre of mass .

Watch Video Solution

λ = A + Bx

11. Find the distance of centre of mass of a uniform cone

of height 'h' and base radius R, from the vertex on the

line of symmetry .

Watch Video Solution

12. A boy standing in a boat �oating on water

is away from the shore of the river. If the boy

moves on the boat towards the shore, then how far

10kg 40kg

20m

8m

is he from the shore ? (Assume no friction between boat

and water).

Watch Video Solution

13. A circular disc of radius R is removed from a bigger

circular disc of radius 2R such that the circumferences

of the discs touch. The centre of mass of the new disc is

at a distance aR from the centre of the bigger disc. The

value of a is

Watch Video Solution

14. A truck of mass travelling at is

brought to rest in when it strikes a wall. What force

(assume constant) is exerted by the wall?

Watch Video Solution

2 × 103kg 4m/s

2s

15. Consider a two particle system with particles having

masses if the �rst particle is pushed

towards the centre of mass through a distance d, by

what distance should the second particle is moved, so

as to keep the center of mass at the same position?

Watch Video Solution

m1 and m2

16. A block of mass M is placed on the top of a bigger

block of mass 10 M as shown in �gure . All the surfaces

are frictionless. The system is released from rest. Find

the distance moved by the bigger block at the instant

the smaller block reaches the ground.

.

Watch Video Solution

17. A disc starts rotating with constant angular

acceleration of about a �xed axis perpendicular

to its plane and through its centre .

(a) Find the angular velocity of the disc after 4s .

(b) Find the angular displacement of the disc after 4 s

and

πrad

s2

(c ) Find number d of turns accomplished by the disc in

4 s .

Watch Video Solution

18. The motor of an engine is erotating about its axis

with an angular velocity of 100 rev/minute. It comes to

rest in 15 s, after being switched o�. Assumgn cnstant

angular decelertion, calculate the number of revolutions

made by it before coming to rest.

Watch Video Solution

19. A wheel is mounted on a stationary axle starts from

rest and is given by the following angular acceleration :

(in SI unit ) where t is the time after the

wheel begins to rotate . Find the number of revolutions

that the wheel turns before it stops ( and begins to turn

in the opposite direction ) .

Watch Video Solution

α = 9 − 12t

20. A wheel rotates with an angular acceleration given

by , where is the time and and are

constants. If the wheel has initial angular speed ,

write the equations for the (a) angular speed (b)

angular displacement.

α = 4at3 − 3bt2 t a b

ω0

Watch Video Solution

21. A �ywheel of radius 30 cm starts from rest and

accelerates with constant with constant angular

acceleration 0.5 . Compute the tangential ,

radial and resultant accelerations of a point on its

circumference :

(a) initially at

(b) after it has made one thrid of a revolution

Watch Video Solution

rad/s2

θ = 0∘

22. A �ywheel rotates with a uniform angular

acceleration. Its angular velocity increases from

to in 10 seconds. How many

rotations did it make in this period ?

Watch Video Solution

20πrad/s 40πrad/s

23. A particle is moving with constant speed v along the

line y = a in positive x -direction. Find magnitude of its

angular velocity about orgine when its position makes

an angle with x-axis.

Watch Video Solution

θ

24. Four point masses lie at the corners of a rectangle

with sides of length 3 m and 4 m ., as shown in �gure .

Find the moment of inertia about of the diagonals . Take

M = 1 kg .

Watch Video Solution

25. Two masses are placed at a distance r

from each other. Find out the moment of inertia of

m1 and m2

system about an axis passing through their centre of

mass.

Watch Video Solution

26. The radius of gyration of a body about an axis at a

distance of from its centre of mass is . Find

its radius of gyration about a parallel axis through its

centre of mass.

Watch Video Solution

12cm 13cm

27. Find the moment of inertia of a circular disc or solid

cylinder of radius R about the following axes .

(a) passing through the centre and perpendicular to the

�at surface .

(b) at the rim and perpendicular to the �at surface

Watch Video Solution

28. Find the moment of inertia of a thin uniform rod

about an axis perpendicular to its length and passing

through a point which is at a distance of from one

end. Also �nd radius of gyration about that axis.

Watch Video Solution

1

3

29. Four thin rods of same mass M and same length l,

form a square as shown in �gure. Moment of inertia of

this system about an axis through centre O and

perpendicular to its plane is

Watch Video Solution

30. To discs have same moment of inertia about their

own axes . Their thickness are also same . If the ratio of

their material densities is 16 :1 . Find the ratio of their

radii .

Watch Video Solution

31. The moment of inertia of a disc, of mass M and

radius R, about an axis which is a tangent and parallel to

its diameter is

Watch Video Solution

32. Four spheres each diameter 2a and mass 'm' are

placed with their centres on the four corners of a

square of the side b. Calculate the moment of inertia of

the system about any side of the square.

Watch Video Solution

33. Find moment of inertia of a sector of mass M , radius

R and of central angle radians .

View Text Solution

θ

34. Find moment of inertia of a sector cut from a disc of

mass M, radius R and central angle

View Text Solution

θ

35. Prove that moment of inertia of an angular sphere

about its diameter . ( Given mass , internal and external

radii are M , respectively ) is

Watch Video Solution

R1 and R2

I = M( )2

5

R52 − R5

1

R32 − R3

1

36. A particle is projected at time from a point

with a speed at an angle to horizontal. Find the

torque of a gravitational force on projectile about the

origin at time plane is vertical plane)

Watch Video Solution

t = 0 O

u θ

t. (x, y

37. Force act at

. Find the net torque of these forces about

Watch Video Solution

2 i + 7j, 2 i + 5j + 7k and i − 2j + k

(4, − 1, 2)

(6, 1, − 3)

38. Find the net torque of these following forces about

origin acting at

acting at

acting at .

Watch Video Solution

→F 1 = i − j

→r1 = 2 i + j,

→F 2 = − i + j

→r2 = i + 2j&

→F 3 = i + j

→r 3 = i − j

39. Find if the force acting

at produces no torque about

Watch Video Solution

α and β→F = 2 i − 3j + k

(2, β, − 1) (α, 0, 2)

40. Find the moment of the couple formed by forces

acting at acting at

Watch Video Solution

5 i + k (9, − 1, 2) and − 5 i − k

(3, − 2, 1)

41. A uniform cube of side a and mass rests on a

rough horizontal table. A horizontal force is applied

normal to one of the faces at a point directly above the

centre of the face, at a height above the base. What

is the minimum value of for which the cube begins to

tip about an edge?

Watch Video Solution

m

F

3a

4

F

42. A griding stone in the form of a solid cylinder has a

radius of 0.5 m and a mass 50 kg . Find

What torque will bring it from rest to an angular

velocity of 300 rev/min in 10 s ?

(b) What is the kinetic energy when it is rotating at 300

rev/min ?

Watch Video Solution

43. Calculate the torque developed by ann airplane

engine whose output is at an angular velocity

of .

Watch Video Solution

2000HP

2400rev/ min

44. A string is wrapped around the rim of a wheel of

moment of inertia 0.20 nd radius 20 cm. The

wheel is free to rotate about it axis. Initially, thewheel is

t rest. The string is now pulled by a force of 20 N. Find

the angular velocity of the wheel after 5.0 seconds.

Watch Video Solution

kg − m2

45. A particle of mass 0.01 kg having position vector

meters is moving with a velocity

m/s . Calculate its angular momentum about the origin.

Watch Video Solution

→r = (10 i + 6j) 5 i

46. A uniform rod of mass m and length l is suspended

by means of two light inextensible strings as shown in

�gure. Tension in one string immediately after the other

string is cut is

Watch Video Solution

47. A ballet dancer spins about a vertical axis at

with arms outstretched. When her arms are folded the

60rpm

angular frequency increases to . Find the change

in her moment of inertia.

Watch Video Solution

90rpm

48. A uniform rod of mass length is allowed to

fall under gravity with in horizontal. When the

speed of the rod is suddenly the end is �xed. Find

the angular velocity with which it begins to rotate.

Watch Video Solution

AB m 2a

AB

v A

49. A turntable turns about a �xed vertical axis, making

one revolution in . The moment of inertia of the10s

turntable about the axis is . A man of ,

initially standing at centre of the turnable, runs out

along the radius. What is the angular velocity of the

turtable when the man is from the centre?

Watch Video Solution

1200kgm2 80kg

2m

50. A cockroach is moving with velocity in

anticlockwise direction on the rim of a disc of radius

of mass . The moment of inertia of the disc about the

axis is and it is rotating in clockwise direction with an

angular velocity . If the cockroach stops, the angular

velocity of the disc will be

Watch Video Solution

v

R

m

I

ω

51. A small block of mass 4 kg is attached to a cord

passing through a hole in a horizontal frictionless

syurface . The block is originally revolving in a circle of

radius 0.5 m about the hole , with a tangential velocity

of 4 m/s . The cord is then pulled slowly from below ,

shortening the radius of the circle in which the block

revolves . The breaking strength of the cord is 600 N .

What will be the radius of the circle when the cord

breaks ?

Watch Video Solution

52. A motor rotates a pulley of radius at 20rpm. A

rope around the pulley lifts a block, What is the

25cm

50kg

power output of the motor?

Watch Video Solution

53. Two small balls A and B each of mass m, are attched

erighdly to the ends of a light rod of length d. The

structure rotates about the perpendicular bisector of

the rod at an angular speed . Calculate the angular

momentum of the individual balls and of the system

about the axis of rotation.

Watch Video Solution

ω

54. A uniform rod of mas m and length l is kept vertical

with the lower end clamed. It is slightly pushed to let it

fall down under gravity. Find its angular speed when the

rod is passing through its lowest positon. Neglect any

friction at the clamp. What will be the linear speed of

the free end at this instant?

Watch Video Solution

55. A rogid body of radius of gyration k and inclined

plane at an angle with horizontal . Calculate its

acceleration and the frictional force acting on it . Also

�nd the expressions for velocity as it reaches the lowest

point and the time taken to reach the lowest point .

θ

View Text Solution

56. A uniform sphere of mass 200 g rols withiout

slipping on a plane surface so that its centre mioves at a

speed of 2.00 cm/s. Find its kinetic energy.

Watch Video Solution

57. A solid sphere rolls without slipping down a

inclined plane. If then the acceleration of

the rolling sphere is

Watch Video Solution

30∘

g = 10ms− 2

58. A uniform solid sphere rolls on a horizontal surface

at . It then rolls up in incline having an angle of

inclination at with the horizontal . If the friction

losses are negligible , the value of height h above the

ground where the ball stops is

Watch Video Solution

20ms− 1

30∘

59. A solid sphere rolls down an inclined plane and its

velocity at the bottom is .The same sphere slides

down the plane (without friction ) and its velocity at the

bottom is . Find the relation between

Watch Video Solution

v1

v2 v1&v2

60. A solid cylinder rolls down an inclined plane of

height and inclination . Calculate its speed to the

bottom of the plane using acceleration method and

energy method. Also calculate the time taken to reach of

the bottom.

Watch Video Solution

h θ