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WORKSHEET FORFRICTION

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Conceptual ProblemsQuestions based on

Q.1 A block is placed on a rough floor and a

horizontal force F is applied on it. The force

of friction f by the floor on the block is

measured for different values of F and a graph

is plotted between them -

(a) The graph is a straight line of slope 45°

(b) The graph is straight line parallel to the

F axis

(c) The graph is a straight line of slope 45º for

small F and a straight line parallel to the

F-axis for large F.

(d) There is small kink on the graph

(A) c, d (B) a, d

(C) a, b (D) a, c

Q.2 Mark the correct statements about the friction

between two bodies -

(a) static friction is always greater than the

kinetic friction

(b) coefficient of static friction is always

greater than the coefficient of kinetic

friction

(c) limiting friction is always greater than the

kinetic friction

(d) limiting friction is never less than static

friction

(A) b, c, d (B) a, b, c

(C) a, c, d (D) a, b, d

Q.3* A block A kept on an inclined surface just

begins to slide if the inclination is 30º. The

block is replaced by another block B and it

is found that it just begins to slide if the

inclination is 40º.

(A) mass of A > mass of B

(B) mass of A < mass of B

(C) mass of A = mass of B

(D) all the three are possible

Q.4 Two cars of unequal masses use similartyres. If they are moving at the same initialspeed, the minimum stopping distance -

(A) is smaller for the heavier car(B) is smaller for the lighter car

(C) is same for both cars(D) depends on the volume of the car

Q.5 Consider the situation shown in figure. Thewall is smooth but the surfaces of A and Bin contact are rough. The friction on B due toA in equilibrium

(A) is upward

(B) is downward

(C) is zero

(D) the system can not remain in equilibrium

Q.6 Suppose all the surfaces in the previousproblem are rough. The direction of frictionon B due to A -

(A) is upward(B) is downward

(C) is zero(D) depends on the masses of A and B

Q.7* A body of mass M is kept on a roughhorizontal surface (friction coefficient = ). Aperson is trying to pull the body by applyinga horizontal force but the body is not moving.The force by the surface on A is F, where -

(A) F = Mg (B) F = Mg

(C) Mg F Mg 1 2

(D) Mg F Mg 1 2

Q.8 In a situation the contact force by a roughhorizontal surface on a body placed on it hasconstant magnitude if the angle between thisforce and the vertical is decreased thefrictional force between the surface and thebody will -

(A) increase(B) decrease

(C) remain the same(D) may increase or decrease

LEVEL # 1

FA B

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Q.9 The contact force exerted by a body A on

another body B is equal to the normal force

between the bodies. We conclude that -

(a) the surfaces must be smooth

(b) force of friction between two bodies may

be equal to zero

(c) magnitude of normal reaction is equal to

that of friction

(d) bodies may be rough

(e) acceleration of two bodies is identical and

remains constant

(A) b, d (B) a, b

(C) c , d (D) a, d

Q.10 It is easier to pull a body than to push,

because -

(A) the coefficient of friction is more in pushing

than that in pulling

(B) the friction force is more in pushing than

that in pulling

(C) the body does not move forward when

pushed

(D) None of these

Motion of Block on the Horizontal Plane

Questions based on

Q.11* A block of metal is lying on the floor of a

bus. The maximum acceleration which can

be given to the bus so that the block may

remain at rest, will be -

(A) g (B) /g

(C) 2g (D) g2

Q.12* A chain is lying on a rough table with a

fraction 1/n of its length hanging down from

the edge of the table. if it is just on the point

of sliding down from the table, then the

coefficient of friction between the table and

the chain is -

(A) 1

n(B)

1

1(n )

(C) 1

1(n ) (D) n

1

1(n )

Q.13* Two masses A and B of 10 kg and 5 kg

respectively are connected with a string

passing over a frictionless pulley at a corner

of a table as shown in the adjoining diagram.

The coefficient of friction of A with the table

is 0.2. The minimum mass of C that may be

placed on A to prevent it from moving is equal to -

C

A

B

(A) 0 kg (B) 5 kg

(C) 10 kg (D) 15 kg

Q.14 In the figure, the block A and B are of masses

3 kg and 2 kg. The coefficient of friction

between the two blocks A and B is 0.3. The

surface of the table is smooth. Then -

(a) The acceleration of masses is 5.75 ms–2

(b) The tensions are T1 and T2 in the strings

are 90.36 N and 17.55 N

(c) Acceleration of masses is 8.15 ms–2

(d) Tension T1 and T2 in the strings are 17.38

N and 40.50 N

(A) a, c (B) c, d

(C) b, d (D) a, d

Q.15* In the arrangement shown mass of A = 1 kg,

mass of B = 2 kg coefficient of friction

between A and B is 0.2. There is no friction

between B and ground. The frictional force

between A and B is: (g = 9.8 ms–2)

(A) 0 N (B) 2 N(C) 1.96 N (D) 1 N

F = 3N

4

Q.16 A block of mass M rests on a rough

horizontal surface as shown. Coefficient of

friction between the block and the surface is

. A force F = Mg acting at angle with the

vertical side of the block pulls it in which of

the following cases the block can be pulled

along the surface ?

(A) tan

(B) tan (/2)

(C) cot (D) cot (/2)

Motion of the block on the inclined Plane

Questions based on

Q.17* The coefficient of friction between car C and

the inclined plane is 0.8. The maximum

acceleration of the car, so that it may move

up the plane inclined at an angle without

slipping will be -

(A) 2.67 m/s2

(B) 3.02 m/s2

(C) 1.88 m/s2

(D) 4.32 m/s2

Q.18 A block rests on a rough inclined plane as

shown in figure. A horizontal force F is applied

to it-

(a) Reaction on the block is F sin + mgcos

(b)Frictional force is zero when

Fcos = mg sin

(c)The value of limiting friction in

(mg sin + F cos )

(d)The value of limiting friction is

(mg sin – Fcos )

(A) a, b (B) c, d

)

F=Mg

M

C

30°

(C) b, d (D) b, c

Q.19 A block moves down a smooth inclined planeof inclination . Its velocity on reaching thebottom is v. If it slides down a rough inclinedplane of some inclination, its velocity onreaching the bottom is v/n, where n is anumber greater than 0. The coefficient offriction is given by -

(A) = tan 112

FHG

IKJn

(B) = cot 112

FHG

IKJn

(C) = tan 112

1 2

FHG

IKJn

/

(D) = cot 112

1 2

FHG

IKJn

/

Q.20* A block of mass 2kg rests on a rough inclinedplane making an angle of 30º with thehorizontal. The coefficient of static frictionbetween the block and the plane is 0.7. Thefrictional force on the block is-(A) 0.7 × 9.8 Newton(B) 9.8 Newton

(C) 0.7 × 9.8 3 Newton

(D) 9.8 × 3 Newton

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Q.1 A 40 kg slab rests on a frictionless floor. A10 kg block rests on top of the slab. Thestatic coefficient of friction between the blockand slab is 0.60 while the kinetic coefficientis 0.40. The 10 kg block is acted upon by ahorizontal force 100 N. If g = 9.8 m/s2, theresulting acceleration of the slab will be -

(A) 0.98 m/s2 (B) 1.47 m/s2

(C) 1.52 m/s2 (D) 6.1 m/s2

Q.2 A lift is moving downwards with anacceleration equal to the acceleration due togravity. A body of mass M kept on the floorof the lift is pulled horizontally. If thecoefficient of friction is , then the frictionalresistance offered by the body is-

(A) Mg (B) Mg(C) 2Mg (D) zero

Q.3 The rear side of a truck is open and box ofmass 20 kg is placed on the truck 4 metersaway from rest with an acceleration of2 m/sec2 on a straight road. The truck startsfrom rest with an acceleration of 2 m/sec2

on a straight road. The box will fall off thetruck when it is at a distance from the start-ing point equal to ( = 0.15) -

(A) 4 m (B) 8 m(C) 16 m (D) 32 m

Q.4 A uniform rope of length l lies on a table ifthe coefficient of friction is , then themaximum length l, of the part of this ropewhich can over hang from the edge of thetable without sliding down is -

(A)

(B)

1

(C)

1 (D)

1

Q.5* A particle is projected along a line of greatestslope on a rough plane inclined at an angleof 45º with the horizontal, if the coefficient offriction is 1/2, then the retardation is-

(A) g

2(B)

g

2 2

(C) g

2 1

1

2F

HGIKJ (D)

g

2 1

1

2F

HGIKJ

Q.6 An inclined plane is inclined at an angle with the horizontal. A body of mass m restson it, if the coefficient of friction is , thenthe minimum force that has to be applied tothe inclined plane to make the body justmove up the inclined plane is -

(A) mg sin (B) mg cos (C) mg cos – mg sin (D) mg cos + mg sin

Q.7 A cart of mass M has a block of mass mattached to it as shown in figure. The coef-ficient of friction between the block and thecart is . What is the minimum accelerationof the cart so that the block m does not fall ?

(A) mg

(B) g

(C) g

(D) M g

m

Q.8 A body A of mass 1 kg rests on a smoothsurface. Another body B of mass 0.2 kg isplaced over A as shown. The coefficient ofstatic friction between A and B is 0.15. B willbegin to slide on A, if A is pulled with a forcegreater than -

(A) 1.764 N

(B) 0.1764 N

(C) 0.3 N

(D) it will not slide for any F

Q.9 A block of mass 1 kg lies on a horizontalsurface in a truck. The coefficient of staticfriction between the block and the surface is0.6 if the acceleration of the truck is 5 m/s2

the frictional force acting on the block is-

(A) 10 N (B) 6 N

(C) 4 N (D) 5 N

LEVEL # 2

10kg40kg

100NNo friction

M m

F

B

A

6

2kg

6kg F

Q.10 Starting from rest, a body slides down a 45ºinclined plane in twice the time it takes toslide down the same distance in the absenceof friction. The coefficient of friction betweenthe body and the inclined plane is -

(A) 0.33 (B) 0.25

(C) 0.75 (D) 0.80

Q.11 A heavy uniform chain lies on a horizontaltable top. If the coefficient of friction betweenthe chain and the table surface is 0.25, thenthe maximum fraction of the length of thechain that can hang over one edge of thetable is -

(A) 20% (B) 25%

(C) 35% (D) 15%

Q.12 A body of mass 2 kg is placed on a horizontalsurface having coefficient of kinetic friction0.4 and coefficient of static friction 0.5. If ahorizontal force of 25 N is applied on thebody, the frictional force acting on the body

will be: (g = 10m

s2 )

(A) 8 N (B) 10 N(C) 20 N (D) 25 N

Q.13 The brakes of a car moving at 20 m/s alonga horizontal road are suddenly applied and itcomes to rest after travelling some distanceif the coefficient of friction between the tyresand the road is 0.90 and it is assumed thatall four tyres behave identically, the shortestdistance the car would travel before comingto a stop is -

(A) 2.27 m (B) 11.35 m(C) 22.7 m (D) 4.54 m

Q.14* A block rests on an inclined plane that makesan angle with the horizontal, if the coefficientof sliding friction is 0.50 and that of staticfriction is 0.75, the time required to slide theblock 4 m along the inclined plane is -

(A) 25 s (B) 10 s

(C) 5 s (D) 2 s

Q.15 Block A has a mass of 2 kg and block B hasa mass of 20 kg if the coefficient of kineticfriction between block B and the horizontalsurface is 0.1, and B is accelerating towardsthe right with a = 2 m/s2, then the mass ofthe block C will be -

(A) 15 kg (B) 12.5 kg(C) 5.7 kg (D) 10.5 kg

Q.16 A force F accelerates a block of mass m onhorizontal surface. The coefficient of frictionbetween the contact surface is . Theacceleration of m will be -

(A) F mg

M

(B) zero

(C) may be (A) or (B) (D) none of these

Q.17 A horizontal force F is exerted on a 20 kgblock to push it up an inclined plane havingan lnclination of 30º. The frictional forceretarding the motion is 80 N. For theacceleration of the moving block to be zero,the force F must be -

(A) 206 N (B) 602 N(C) 620 N (D) 260 N

Q.18 With reference to the fig. shown, if thecoefficient of friction at all the surfaces is0.42, then the force required to pull out the6.0 kg block with an acceleration of 1.50 m/s2

will be -

(A) 36 N (B) 24 N(C) 84 N (D) 51 N

Q.19 A person wants to drive on the vertical surfaceof a large cylindrical wooden 'well' commonlyknown as 'death well' in a circus. The radiusof the well is R and the coefficient of frictionbetween the tyres of the motorcycle and thewall of the well is s. The minimum speedthe motor cyclist must have in order toprevent slipping should be -

(A) gR

s(B)

s

gR

(C) sg

R(D)

R

gs

A C

B

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Q.20 A spherical ball of mass 1/2 kg is held at thetop of an inclined rough plane making angle30º with the horizontal the coefficient oflimiting friction is 0.5. If the ball just slidesdown the plane without rolling its accelerationdown the plane is -

(A) 2 3

4

LNMM

OQPP g (B) g

(C) 2 3 1

4

LNMM

OQPP g (D)

3 1

2

LNMM

OQPP g

Q.21 An object is placed on the surface of asmooth inclined plane of inclination . It takestime t to reach the bottom of the inclinedplane. If the same object is allowed to slidedown rough inclined plane of same inclination, it takes time nt to reach the bottom wheren is a number greater than 1. The coefficientof friction is given by -

(A) = tan 112

FHG

IKJn

(B) = cot 112

FHG

IKJn

(C) = tan 112

1 2

FHG

IKJn

/

(D) = cot 112

1 2

FHG

IKJn

/

Q.22 A given object takes n times as much timeto slide down a 45º rough incline as it takesto slide down a perfectly smooth 45º incline.The coefficient of kinetic friction between theobject and the incline is given by -

(A) 1 – 12n

(B) 1

1 2 n

(C) 112

n

(D) 1

1 2 n

Q.23 A 15 kg mass is accelerated from rest witha force of 100 N. As it moves faster, frictionand air resistance create an oppositivelydirected retarding force given by FR = A + Bv,where A = 25 N and B = 0.5 N/m/s. At whatvelocity does the acceleration equal to onehalf of the initial acceleration?

(A) 25 ms–1 (B) 50 m/s(C) 75 m/s (D) 100 m/s

Q.24 Two blocks of masses M = 3 kg andm = 2 kg, are in contact on a horizontaltable. A constant horizontal force F = 5 N isapplied to block M as shown. There is aconstant frictional force of 2 N between thetable and the block m but no frictional forcebetween the table and the first block M, thenthe acceleration of the two blocks is-

(A) 0.4 ms–2 (B) 0.6 ms–2

(C) 0.8 ms–2 (D) 1 ms–2

Q.25 Starting from rest a body slides down a 45ºinclined plane in twice the time it takes toslide down the same distance in the absenceof friction. The coefficient of friction betweenthe body and the inclined plane is -

(A) 0.33 (B) 0.25(C) 0.75 (D) 0.80

Q.26* Block A of mass M in the system shown inthe figure slides down the incline at a

constant speed. The coefficient of friction

between block A and the surface is 1

3 3.

The mass of block B is-

(A) M/2 (B) M/3(C) 2M/3 (D) M/ 3

F M m

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Q.27 Two blocks connected by a massless string

slide down an inclined plane having angle of

inclination 37º. The masses of the two blocks

are M1 = 4 kg and M2 = 2 kg respectively

and the coefficients of friction 0.75 and 0.25

respectively-

(a) The common acceleration of the two

masses is 1.3 ms–2

(b) The tension in the string is 14.7 N

(c) The common acceleration of the two

masses is 2.94 ms–2

(d) The tension in the string is 5.29 N

(A) a, d (B) c, d

(C) b, d (D) b, c

Q.28 The coefficient of static friction between the

two blocks is 0.363. What is the minimum

acceleration of block 1 so that block 2 does

not fall ?

(A) 6 ms–2 (B) 12 ms–2

(C) 18 ms–2 (D) 27 ms–2

Q.29 A block of mass m is placed on a rough

inclined plane of inclination kept on the

floor of the lift. The coefficient of friction

between the block and the inclined plane is

. With what acceleration will the block slide

down the inclined plane when the lift falls

freely ?

(A) Zero

(B) g sin – g cos

(C) g sin + g cos

(D) None of these

Q.30 Block A of mass 35 kg is resting on a

frictionless floor. Another block B of mass

7 kg is resting on it as shown in the figure.

The coefficient of friction between the blocks

is 0.5 while kinetic friction is 0.4. If a force

of 100 N is applied to block B, the

acceleration of the block A will be

(g = 10 m s–2) :

(A) 0.8 m s–2 (B) 2.4 m s–2

(C) 0.4 m s–2 (D) 4.4 m s–2

Q.31* A box of mass 8 kg is placed on a rough

inclined plane of inclination . Its downward

motion can be prevented by applying an

upward pull F and it can be made to slide

upwards by applying a force 2F. The

coefficient of friction between the box and

the inclined plane is -

(A) 3

1 tan (B) 3 tan

(C) 2

1 tan (D) 2 tan

Q.32 A wooden block of mass M resting on a rough

horizontal surface is pulled with a force F at

an angle with the horizontal. If is the

coefficient of kinetic friction between the block

and the surface, then acceleration of the

block is -

(A) M

F (cos + sin ) – g

(B) F sin /M

(C) F cos

(D) F sin

a1 2

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Each of the questions given below consistof Statement – I and Statement – II. Usethe following Key to choose theappropriate answer.(A) If both Statement- I and Statement- II

are true, and Statement - II is the correctexplanation of Statement– I.

(B) If both Statement - I and Statement - IIare true but Statement - II is not thecorrect explanation of Statement – I.

(C) If Statement - I is true but Statement - II is false.(D) If Statement - I is false but Statement - II

is true.

Q.33 Statement I : Pulling a lawn roller is easierthan pushing it.

Statement II : Pushing increases the apparentweight and hence force of friction.

Q.34 Statement I : The force of friction in the caseof a disc rolling without slipping down an inclinedplane is zero.

Statement II : When the disc rolls withoutslipping, friction is required because for rollingcondition velocity of point of contact is zero.

Q.35 Statement I : Friction is self adjusting force.

Statement II : The magnitude of static friction

is equal to the applied force and its direction is

opposite to that of the applied force.

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Q.1 A block of mass 4 kg is kept over a rough

horizontal surface. The coefficient of friction

between the block and the surface is 0.1. At

t = 0, 3 m/s )i( velocity is imparted to the

block and simultaneously 2N )i( force

starts acting on it. Its displacement in first 5

second is (g = 10 m/s2) -

(A) i8 (B) i8

(C) i3 (D) i3

Q.2 In the given figure the wedge is fixed, pulley is

frictionless and string is light. Surface AB is

frictionless whereas AC is rough. If the block

of mass 3m slides down with constant velocity,

then the coefficient of friction between surface

AC and the block is -

(A) 3

1(B)

3

2(C)

2

1(D)

3

4

Q.3 Mass of upper block and lower block kept over

the table is 2 kg and 1 kg respectively and

coefficient of friction between the blocks is 0.1.

Table surface is smooth. The maximum mass

M for which all the three blocks move with

same acceleration is (g = 10 m/s2) -

(A) 1 kg (B) 2/3 kg

(C) 1/3 kg (D) 3/4 kg

LEVEL # 3Q.4 A block of mass m lying on a rough horizontal

plane is acted upon by a horizontal force Pand another force Q inclined at an angle tothe vertical. The block will remain in equilibriumif the coefficient of friction between it and thesurface is -

(A)

cosQmg

sinQP(B)

sinQmg

QcosP

(C)

sinQmg

cosQP(D)

cosQmg

QsinP

Q.5 A block slides down an inclined surface ofinclination 30º with the horizontal. Starting fromrest it covers 8m in the first two seconds. Findthe coefficient of kinetic friction between thetwo.

(A) 0.11 (B) 0.5 (C) 0.8 (D) 0.2

Q.6 A body of mass 2 kg is lying on a rough inclinedplane of inclination 30º. Find the magnitude ofthe force parallel to the incline needed to makethe block move (a) up the incline (b) down theincline. Coefficient of static friction = 0.2

(A) 13 N, 5 N (B) 13 N, 13 N

(C) 13 N, 0 N (D) 5 N, 13 N

Q.7 Figure shows two blocks in contact slidingdown an inclined surface of inclination 30º. Thefriction coefficient between the block of mass2.0 kg and the incline is µ1, and that betweenthe block of mass 4.0 kg and the incline is µ2.Calculate the acceleration of the 2.0 kg blockif µ1 = 0.30 and µ2 = 0.20, Take g = 10 m/s2

30º

4 kg

2 kg

(A) 2 m/s2 (B) 2.7 m/s2

(C) 4 m/s2 (D) 2.4 m/s2

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Q.8 A box of mass 8 kg is placed on a roughinclined plane of inclination . Its downwardmotion can be prevented by applying an upwardpull F and it can be made to slide upwards byapplying a force 2F. The coefficient of frictionbetween the box and the inclined plane is -

(A) 3

1 tan (B) 3 tan

(C) 2

1 tan (D) 2 tan

Assertion/Reason Type Questions

Each of the questions given below consistof Statement – I and Statement – II. Usethe following Key to choose theappropriate answer.(A) If both Statement- I and Statement- II

are true, and Statement - II is the correctexplanation of Statement– I.

(B) If both Statement - I and Statement - IIare true but Statement - II is not thecorrect explanation of Statement – I.

(C) If Statement - I is true but Statement - II is false.(D) If Statement - I is false but Statement - II is true.

Q.9 Assertion : A coin is placed on phonogramturn table. The motor is started, coin movesalong the moving table.

Reason : Rotating table is providing necessarycentripetal force to the coin.

(A) a (B) b

(C) c (D) d

Q.10 Assertion : By pressing a block against arough wall, one can balance it.

Reason : Smooth walls can not hold the blockby pressing the block against the wall, howeverhigh the force is exerted.

(A) a (B) b

(C) c (D) d

Q.11 Assertion : The value of dynamic friction isless than the limiting friction.

Reason : Once the motion has started, theinertia of rest has been overcome.

(A) a (B) b

(C) c (D) d

Q.12 Assertion : The acceleration of a body downa rough inclined plane is greater than theacceleration due to gravity.

Reason : The body is able to slide on a inclinedplane only when its acceleration is greater thanacceleration due to gravity

(A) a (B) b

(C) c (D) d

Column matching Type QuestionsQ.13 A man is standing on a ladder as shown in

figure. N1 and N2 are the normal reactions andf the force of friction. Then match the followingtable:

Roughf

Smooth N1

N2

Table -1 Table -2

(A) As the man moves (P) N1 will increase

up the ladder

(B) If weight of ladder is (Q) N1 will decrease

increased (R) N2 will increase

(S) N2 will decrease

(T) f will increase

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LEVEL # 4(Approximately 4 mins for each Question)SECTION - A

Q.1 A horizontal force of 10 Newton is necessary

to just hold a block stationary against a wall.

The coefficient of friction between the block and

the wall is 0.2. The weight of block is –

(A) 50 N (B) 100 N

(C) 2 N (D) 20 N

Q.2 A marble block of mass 2 kg lying on ice when

given a velocity of 6 m/s is stopped by friction

is 10 s. Then the coefficient of friction is –

(A) 0.03 (B) 0.04

(C) 0.06 (D) 0.02

Q.3 A block rests on a rough indined plane making

an angle of 30° with the horizontal. The

coefficient of static friction between the block

and the plane is 0.8. If the frictional force on the

block is 10 N, the mass of block (in kg) is

(Take g = 10 m/s2)

(A) 2.0 (B) 4.0

(C) 1.6 (D) 2.5

Q.4 A smooth block is released at rest on a 45º incline

and then slides a distance 'd'. The time taken to slide

is 'n' times as much to slide on rough incline than on

a smooth incline. The coefficient of friction is

(A) µK = 1 – 2n

1(B) µk= 2n

11

(C) µS = 2n

11 (D) µS = 2n

11

Q.5 The upper half of an inclined plane withinclination is perfectly smooth while the lowerhalf is rough. A body starting from rest at thetop will again come to rest at the bottom if thecoefficient of friction for the lower half is givenby(A) 2 sin (B) 2 cos (C) 2 tan (D) tan

SECTION - BQ.1 A block of mass 0.1 kg is held against a wall

by applying a horizontal force of 5 N on theblock. If the coefficient of friction between theblock and the wall is 0.5 , the magnitude ofthe frictional force acting on the block is –

(A) 2.5N (B) 0.98 N(C) 4.9 N (D) 0.49 N

Q.2 A cubical block of side L rests on a roughhorizontal surface with coefficient of friction. A horizontal force F is applied on the blockas shown. If the coefficient of friction issufficiently high so that the block does notslide before toppling , the minimum forcerequired to topple the block is

F

L

(A) infinitesimal (B) mg/4(C) mg/2 (D) mg (1 - )

Q.3 A long horizontal rod has a bead which canslide its length, and initially placed at a distanceL from one end A of the rod. The rod is set inangular motion about A with constant angularacceleration a. If the coefficient of frectionbetween the rod and the bead is , and gravityis neglected, then the time after which the beadstarts slipping is :

(A)

(B)

(C)

1(D) infinitesimal

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Q.4 A block of mass 32 kg is placed on a rough

horizontal surface whose coefficient of friction

is 32

1. Then the minimum value of force F

(shown in figure) for which the block starts toslide on the surface. (g = 10m/s2 )

(A) 10N (B) 5N

(C) 40N (D) N3

20

Q.5 Two blocks P & Q of same mass m areplaced as shown in figure. Coefficient ofstatic friction between P & Q is s . There isno friction between P and horizontal surface.The block system is displaced by a distanceA and released. If there is no slippingbetween Q & P then maximum value offriction on block P is

(A) 0 (B) K A(C) KA /2 (D) s mg

Q.6 A force F is applied on the square block ofedge length 2a such that block remainsstationary on the vertical wall. Then falsestatement is

a

a

F

(A) f = mg, where f is frictional force

(B) F = N, where N is normal reaction

(C) F does not produce any torque

(D) N does not produce any torque

Q.7 A disc having a groove as shown in kept on

smooth horizontal plane. A block of mass m

can slide in the groove. The disc move with

acceleration a0 = 25 m/s2 as shown in figure.

The coefficient of friction between block and

groove is 2/5 and sin = 3/5. Find the

acceleration of block relative to the disc.

m)

a0 = 25m/s2

Q.8 STATEMENT - 1

A block of mass m starts moving on a rough

horizontal surface with a velocity v. It stops

due to friction between the block and the

surface after moving through a certain

distance. The surface is now tilted to an angle

of 30º with the horizontal and the same block

is made to go up on the surface with the

same initial velocity v. The decrease in the

mechanical energy in the second situation is

smaller than that in the first situation.

Because

STATEMENT - 2

The coefficient of friction between the block

and the surface decreases with the increase in

the angle of inclination.

(A) Statement-1 is True, Statement-2 is True;

Statement-2 is a correct explanation for

Statement-1

(B) Statement-1 is True, Statement-2 is True;

Statement-2 is NOT a correct explanation for

Statement-1

(C) Statement-1 is True, Statement-2 is False

(D) Statement-1 is False, Statement-2 is

True.

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Q.9 STATEMENT –1

A cloth covers a table. Some dishes are kepton it. The cloth can be pulled out withoutdislodging the dishes from the table.

because

STATEMENT –2

For every action there is an equal andopposite reaction.

(A) Statement–1 is True, Statement–2 isTrue; Statement–2 is a correct explanationfor Statement–1

(B) Statement–1 is True, Statement–2 is True;Statement–2 is NOT a correct explanation forStatement–1

(C) Statement–1 is True, Statement–2 isFalse

(D) Statement–1 is False, Statement–2 isTrue.

Q.10 STATEMENT - 1It is easier to pull a heavy object than to pushit on a level ground.andSTATEMENT - 2The magnitude of frictional force depends onthe nature of the two surfaces in contact.(A) STATEMENT-1 is True, STATEMENT-2 is

True; STATEMENT-2 is a correct explana-tion for STATEMENT-1

(B) STATEMENT-1 is True, STATEMENT-2 isTrue; STATEMENT-2 is NOT a correctexplanation for STATEMENT-1

(C) STATEMENT-1 is True, STATEMENT-2 isFalse

(D) STATEMENT-1 is False, STATEMENT-2 isTrue

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ANSWER KEY

LEVEL # 2

LEVEL # 1

Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ans. A A D C D A C B A B A B D D D

Q.No. 16 17 18 19 20

Ans. D C A A B

LEVEL # 3Q.No. 1 2 3 4 5 6 7 8 9 10 11 12

Ans. C B D A A C D D A B A D A (P,T) B (P,T,R)

13

LEVEL # 4

SECTION - A

1 2 3 4 5

C C A A C

SECTION - B

Q.No. 1 2 3 4 5 6 7 8 9 10

Ans. C C A C C D 10 B B B

Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Ans. A D C C C D B A D C A A C D D C A D

Q.No. 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Ans. A A A A C B C B A D A A A A A D D