NEET UG Physics Properties of Liquid of Solid MCQs

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Unit - 7Proporties ofLiquid a Solid

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SUMMARY

Surface tension of a liquid is measured by the forceacting per unit length on either side of an imaginary linedrawn on the free surface of liquid, the direction of thisforce being perpendicular to the line and tangential tothe free surface of liquid. So if F is the force acting onone side of imaginary line of length l. then T = Fl.

1. It depends only on the nature of liquid and is independent of the area of surface or length of lineconsidered.

2. It is a scalar as it has a unique direction which is not to be specified.

3. Dimension 201 TLM

4. Unit : SImN

5. It is a molecular phenomenon and its root cause is the electromagnetic forces.

Force Due to Surface TensionIf a body of weight W is placed on the liquid surface, whose surface tension is T, and if F is theminimum force required to pull it away from the water then value of F for different bodies can becalculated by the following table.

Body Force

1. Needle (length l) wT2F

2. Hollow disc (inner radius r1 Outer radius r2) wTrr2F 21

3. Thin ring (radius r) wrT4F

4. Circular plate (or disc) (radius r) wrT2F

5. Square frame (side l) wT8F

6. Square plate wT4F Examples of Surface Tension :

1. When mercury is split on a clean glass plate, it formsglobules. Tiny globules are spherical on the account ofsurface tension because force of gravity is negligible. Thebigger globules because force of gravity is negiligible. Thebigger globules get plattened from the middle but haveround shape near the edges.



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2. When a molten metal is poured into water from asuitable height, the falling stream of metal breaks upand the detached portion of the liquid in small quantityacquire the spherical shape.

3. Rain drops are spherical in shape because each drop tends to acquire minimum surface area due tosurface tension, and for a given volume, the surface area of sphere is minimum.

4. Oil drop spreads on cold water. Whereas it may remain as a drop on hot water. This is due to thefact that the surface tension of oil is less than that of cold water and is more than that of hot water.

5. If a small irregular piece of camphor is floated on the surface of pure water, it does not remain steadybut dances about on the surface. This is because, irregular shaped camphor dissolves unequally anddecreases the surface tension of the water locally. The unbalanced forces make it to move haphazardlyin different directions.

6. Take a frame of wire and dip it in soap solutionand take it out, a soap film will be formed in theframe. Place a loop of wet thread gently on thefilm. It will remain in the form, we place it on thefilm according to figure.Now, piercing the film with a pin at any pointinside the loop, It immediately takes the circularfrom as shown in figure.

7. When a greased iron needle is placed genetly on the surface ofwater at rest, so that it does not prick the water surface, the needlefloats on the surface of water despite it being heavier because theweight of needle is balanced by the vertical components of the forcesof surface tension. If the water surface is pricked by one end of theneedle, the needle sinks down.

8. Hair of shaving brush / painting brush when dipped inwater spread out, but as soon as it is taken out, its hairstick together.

Factors affecting surface tension1. Temperature :

The surface tension of liquid decreases with rise of temperature. The surface tension of liquid is zeroat its boiling point and it vanishes at critical temperature. At critical temperature, intermolecularforces for liquid and gases becomes equal and liquid can expand without any restriction. For smalltemperature differences, the variation in surface tenstion with temperature is linear and is given bythe relation.



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t1TT 0t

Where Tt and TO are the surface tensions at tOc and 0OC respectively and is the temperaturecoefficient of surface tension.Examples :(i) Hot soup tastes better than the cold soup.(ii) Machinery parts get jammed in winter.

2. Impurities :The presence of impurities either on the liquid surface or dissolved in it, considerably affect thesurface tension, depending upon the degree of contamination. A highly soluble substance like sodiumchloride when dissolved in water, increases the surface tension of water. But the sparingly solublesubstances like phenol when dissolved in water, decreases the surface tension of water.Applications of Surface Tension

1. The oil and grease spots on cloths cannot be removed be pure water. On the other hand, whendetergents (like soap) are added in water, the surface tension of water decreases. As a result of this,wetting power of soap solution increases. Also the force of adhesion between soap solution and oilor grease on the clothes increases. Thus, Oil, grease and dirt particles get mixed with soap solutioneasily. Hence, clothes are washed easily.

2. Surface tension of all lubricating oils and paints is kept low so that they spread over a large area.3. A rough sea can be calmed by pouring oil on its surface.4. In soldering, addition of 'flux' reduces the surface tension of molten tin, hence, it spreads.

Molecular Theory of Surface TensionThe maximum distance upto which the force of attraction betweentwo molecules is appriciable is called molecular range m10 9 .A sphere with a molecule as centre and radius equal to molecularrange is called the sphere of influence. The liquid enclosed betweenfree surface (PQ) of the liquid and an imaginary plane (RS) at adistance r (equal to molecular range) from the free surface of theliquid form a liquid film.To understand the concept of tension acting on the free surface of a liquid, let us consider four liquidmolecules like A, B, C and D. Their sphere of influence are shown in the figure.

1. Molecule A is well within the liquid, so it is attracted equally in all directions. Hence the net force onthis molecule is zero and it moves freely inside the liquid.

2 Molecule B is little below the free surface of the liquid and it is also attracted equally in all directions.Hence the resultant force acting on it is also zero.

3. Molecule C is just below the upper surface of the liquid film and the part of its sphere of influence isoutside the free liquid surface. So the number of molecules in the upper half (attracting the moleculesupward) is less than the number of molecule in the lower half (attracting the molecule downward).Thus the molecule C experiences a net downward force.

4. Molecule D is just on the free surface of the liquid. The upper half of the sphere of influence has noliquid molecule. Hence the molecule D experiences a maximum downward force.



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Thus all molecules lying on surface film experiences a net downward force. Therefore, free surfaceof the liquid behaves like a stretched membrane.Surface Energy :The potential energy of surface molecules per unit area of the surface is called surface energy.

Unit : 2mJ

Dimension : 2ML

Suppose that the sliding wire LM is moved through asmall distance x, so as to take me position . .ML Inthis process, area of the film increases by x2 (onthe two sides) and to do so, the work done is given by,

ATx2Tx2TfxW

AWT

i.e. Surface tension may be defined as the amount of work done in increasing the area of the liquidsurface by unity against the force of surface tension at constant temperature.Work done in Blowing a liquid drop or soap-bubble

1. If the intial radius of liquid drop is r1 and the final radius of liquid drop is r2 then,

AreainincrementTW

21

22 rr4T

2. In case of soap-bubble,

21

22 rr8TW (Bubble has two free surfaces)

Splitting of Bigger Drop :When a drop of radius R splits into n smaller drops, (each of radius r) then surface area of liquidincreases. Hence the work is to be done against surface tension.Since the volume of liquid remains constant therefore

33 r34nR

34

33 nrR

Work done AT 22 R4rn4T

Formation of Bigger drop :Amount of surface energy released = Initial surfaceenergy - final surface energy

TR4nTr4E 22

Excess Pressure :Due to the property of surface tension a drop or bubble tends to contract and so compresses thematter enclosed. This in turn increases the internal pressure which prevents further contraction and



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equilibrium is achieved. So in equilibrium the pressure inside a bubble or drop is greater than outsideand the difference of pressure between two sides of the liquid surface is called excess pressure.Excess pressure in different cases is given in the following table :Plane surface Concave surface

P = 0 P = 2TR

Convex surface Drop

P = 2TR P =

2TR

Bubble in air Bubble in liquid

P = 4TR P =

2TR

Cylindrical liquid surface Liquid film of unequal radii

RIP

21 R1

R1T2P

Shape of liquid meniscus :When a capillary tube is dipped in a liquid, the liquid surface becomes curved near the point ofcontact. This curved surface is due to the resultant of two force i.e. the force of cohesion and theforce of adhesion. The curved surface of the liquid is called meniscus of the liquid.If liquid molecule A is in the contact with solid. (i.e. wall of capillary tube) then forces acting onmolecule A are(i) Force of adhesion Fa

(ii) Force of cohesion FC

(iii) Resultant force FN makes an angle with Fa.

Ca

Co

Ca

oC

FF2F

135cosFF135sinFtan

Example :Pure water in silver coated capillary tube.



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Angle of contact :Angle of contact between a liquid and a solid is defined as the angle enclosed between the tangentsto the liquid surface and the solid surface inside the liquid, both the tangents being drawn at the pointof contact of the liquid with the solid.Capillarity :If a tube of very narrow bore is dipped in a liquid, it is found that the liquid in the capillary eitherascends or descends relative to the surrounding liquid. This phenomenon is called capillarity.The root cause of capillarity is the difference in pressure on two sides of (concave and convex)curved surface of liquid.Examples :(i) Ink rises in the fine pores of bloting paper leaving the paper dry.(ii) A towel soaks water.(iii) Oil rises in the long narrow spaces between the threads of wick.

Ascent Formula :

2ThρgR

rhρg RhρgT2cosθ 2

Useful Facts and Formulae :(1) Formation of double bubble :

Radius of the interface 1...rr

rrr12

21

and 2...r1

r1T4P

21

(2) Formation of a single bubbleUnder isothermal condition two soap bubble of radii "a"and "b" coalesce to from a single bubble of radius C.

Now CT4PP,

bT4PP,

aT4PP 0C0b0a

3a a

34V

Now as mass is conserved,

3c c

34V

cba

3c c

34V

c

cc

b

bb

a

aa

RTVP

RTVP

RTVP



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Temp is constant,

cba TTT

3

003

0 c34

CT4P

bT4Pa

34

aT4P

222

3330

cba4bacPT

Hooke's Law and Modulus of Elasticity :According to this Law, within the elastic limit, stress is proportional to the strain.i.e. stress strain

StressStrain

= E = constant

The constant E is called the modulus of elasticity.There are three modulii of elasticity namely (i) Young'smodulus (y), (ii) Bulk modulus (B), and modulus of rigidity(), responding to three types of the strain.

(1) Young's modulus (Y)It is defined as the ratio of normal stress to longitudinal strain within limit of proportionality

AFL

L

AF

strainallongitudinstressNormalY

2rmgLY

Force constant of wire,

LYAFK

Bulk Modulus :When a solid or fluid (liquid or gas) is subjected to a uniform pressure all over the surface, such thatthe shape remains the same, then there is a change in volume.Then the ratio of normal stress to the volumetric strain within the elastic limits is called as Bulkmodulus. This is denoted by K.

strainVolumetricstressNormalK

vpV

Vv

AF



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Modulus of Rigidity :Within limits of proportionality, the ratio of tangential stress to the shearing strain is called modulus ofrigidity of the material of the body and is denoted by ,

strainShearingstressTangential

In this case the shape of a body changes but its volume remains unchanged.

AFA

F

Pascal's Law :It states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest issame.Working of hydraulic lift, hydraulic press and hydroulic breaks :It is used to lift the heavy loads. If a small force f isapplied on pistion of C then the pressure exerted onthe liquid

afP

[a = Area of cross section of the pistion in C]This pressure is transmitted equally to piston of cylinder D.

AfA

afPAF As A >> a, F << f

Thermal Expansion :When matter is heated without any change in its state it usually expands. According to atomic theoryof matter, a symmetry in potential energy curve is responsible for thermal expansion. As energy ofatoms increases, hence the average distance between the atoms increases. So the matter as a wholeexpands.

(1) Thermal expansion is minimum in case of solids but maximum in case of gases because intermolecularforce is maximum in solids but minimum in gases.

(2) Solids can expand in one dimension (linear expansion) two dimensions (superficial expansion) andthree dimensions (volume expansion) While liquids and gases usually suffer change in volume only.Heat :

(1) The form of energy which is exchanged among various bodies or system on account of temperaturedifference is defined as heat.

(2) We can change the temperature of a body by giving heat (temperature rises) or by removing heat(temperature falls) from body.

(3) Heat is a scalar quantity. It's units are joule, erg, cal, kcal etc.(4) 1 kcal = 1000 cal = 4186 J and 1 cal = 4.18 J



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Specific Heat :(1) The amount of heat energy required to raise the temperature of unit mass of a body through (or K)

is called specific heat of the material of the body.

If Q heat changes the temperature of mass m by then specific heat

mC

122 TLUnit (2) Molar specific Heat :

Molar specific heat of a substance is defined as the amount of heat required to raise the temperatureof one gram mole of the substance through a unit degree, it is represented by C

Q1QmM

MMQC

Unit : 1221 TLM

(3) Latent Heat :The amount of heat required to change the state of the mass m of the substance while its temperatureremaining constant is written as : Q = mL, where L is the latent heat Latent heat is also called as

Heat of Transformation, It's unit is gmcal

or kgJ

and dimension : 22 TL

Elastic behaviour :The propertory of matter by virture of which a body

tends to regain its original shape and size after the removal ofdeforming force is called elasticity.

In solids, atoms and molecules are arranged in such away that each molecule is acted upon by the forces due toheighbouring molecules. These forces are known asintermolecular forces.

For simplicity, the two molecules in their equilibrium positions (at inter-molecular distancer = r0) are shown by connecting them with a spring.

In fact, the spring connecting the two molecules represents the inter-molecular force betweenthem on applying the deforming forces, the molecules either come closer or go far apart from eachother and restoring forces are developed. When the deforming force is removed, these restoringforces bring the molecules of the solid to their respective equilibrium position (r = r0) and hence thebody regains its original form.Thermal Capacity : It is defined as the amount of heat required to raise the remperature of the whole body (mass m)through 10C or 1K.

Thermal capacity

Qcmc

The value of thermal capacity of a body depends upon the nature of the body and its mass.

Dimensions 1221 TLM Units : kJ,

CCalo



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Principle of Calorimetry :Calorimetry means 'measuring heat'.When two bodies (one being solid and other liquid or both being liquid) at different temperatures aremixed, heat will be transfered from body at higher temperature to a body at lowe temperature tillboth acquire same temeprature. The body at higher temperature releases heat while body at lowertemeprature absorbs it, so that

Heat lost = Heat gainedi.e., Principle of calorimetry represents the law of conservation of heat energy.Thermometry :A branch of science which deals with the measurement of temperature of a substance is known asthermometry.Phase change :

We use the term phase to describe a specific state of matter, such as solid, liquid or gas. Atranstion from one phase to another is called a phase change.

For any given pressure a phase change takes place at a definite temperature, usuallyaccompanied by absorption or emission of heat and a change of volume and density.

In phase change 10ce at 00C melts into water at 00C. Water at 1000C boils to form steam at1000C.Streamline flow :

Stream line flow of a liquid is that flow in which each element of the liquid passing through apoint travels along the same path and with the same velocity as the preceding element passes throughthat point.

A streamline may be defined as the path, straight orcurved, the tangent to which at any point gives the directionof the flow of liquid at that point.

The two streamlines cannot cross each other andthe greater is the crowding of streamlines at a place, thegreater is the velocity of liquid particles at that place.Laminar Flow :

If a liquid is flowing over a horizontal surface with a steady flow and moves in the form oflayers of different velocities which do not mix with each other, then the flow of liquid is called laminarflow.

In this flow, the velocity of liquid flow is always less than the critical velocity of the liquid. Thelaminar flow is generally used synonymously with streamlined flow.Turbulent flow :

When a liquid, moves with a velocity greater thanits critical velocity, the motion of the particles of liquidbecome disordered or irregular. Such a flow is called aturbulent flow.

In a turbulent flow, the path and the velocity of the particles of the liquid change continuouslyand haphazardly with time from point to point. In a turbulent flow, most of the external energy



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maintaining the flow is spent in producint eddies in the liquid and only a small fraction of energy isavailable for forward flow.Critical velocity :

The critical velocity is that velocity of liquid flow upto which its flow is streamlined and abovewhich its flow becomes turbulent.Reynold's number :

Reynold's number is a pure number whichdetermines the nature of flow of liquid through apipe.

areaunitperforceViscousareaunitperforceInprtialNR

3AVdtdmNow

Inertial force per unit area AdtdmV

Adtd

2VAAVV

Viscous force per unit area rnv

AF

VrNR

If ,2000N0 R If 3000N2000 R If 3000NR

laminar or stream line Unstable flow definitely turbulent flowEquation of continuity :

The equation of continuity is derived from theprinciple of conservation of mass.

A non-viscous liquid in streamline flow passesthrough a tube AB of varying cross section. Let the crosssectional area of the pipe at points A and B be a1 and a2respectively.

Mass of the liquid entering per second at A = Massof the liquid leaving per second at B.

222111 vava 2211 vava

If the liquid is incompressible av = constantwhich is the equation of continuity.



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MCQFor the answer of the following questions choose the correct alternative from amongthe given ones.1. Two wires are made of the same material and have the same volume. However, wire 1 has cross-

sectional area A and wire 2 has cross-sectional Area 3A. If the length of wire 1 increases by onappling force F. How much force is needed to stretch wire 2 by same amount.(A) F (B) 4F (C) 6F (D) 9F

2. The increases in length in l of a wire of length L by longitudinal stress. Then the stress is propotionalto..............

(A) L

(B) L (C) (D) L2

3. The dimensions of four wires of the same material are given below, in which wire the increase inlength will be maximum when the same strain is applied.(A) Length 100 cm, Diameter 1 mm (B) Length 200 cm, Diameter 2 mm(C) Length 300 cm, Diameter 3 mm (D) Length 50 cm, Diameter 0.5 mm

4. The young's modulus of a wire of length L and radius r is Y 2mN

. If the length and radius are

reduced to 2L

and 2r

. Then what will be its young's modulus ?

(A) 2Y

(B) Y (C) 2Y (D) 4Y

5. A beam of metal supported at the two ends is loaded at the centre. The depression at the centre ispropotional to..............

(A) Y2 (B) Y (C) Y1

(D) 2Y1

6. A wire is loaded by 6 kg at its one end, the increase in length is 12 mm. If the radius of the wire isdoubled and all other magnitudes are unchanged, then increase in length will be.............(A) 6 mm (B) 3 mm (C) 24 mm (D) 48 mm

7. On increasing the length by 0.5 mm in a steel wire of length 2 m and area of cross-section 2 mm2 theforce required is................

[Y for steel mN102.2 11 ]

(A) N101.1 5 (B) N101.1 4 (C) N101.1 3 (D) N101.1 2

8. A stress of 28 Nm1018.3 is applied to steel rod of length 1 m along its length. Its young's

modulus is 211

mN102 . Then what is the elongation produced in the rod in mm ?

(A) 3.18 (B) 6.36 (C) 5.18 (D) 1.59



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9. Two springs P & Q of force constant KP & KQ PQ

KK2

are stretched by applying force equal

magnitude. If the energy stored in Q is E. Then what is the energy stored in P ?

(A) E (B) 2E (C) 2E

(D) 4E

10. A force F is needed to break a copper wire having radius R, The force needed to break a copperwire of radius 2R will be........

(A) 2F

(B) 2F (C) 4F (D) 4F

11. A rubber cord 10m long is suspended vertically. How much does it stretch under its own weight.

( Density of rubber is 22

83 s

m10g,mN105Y,

mkg1500 )

(A) m1015 4 (B) m105.7 4 (C) m1012 4 (D) m1025 4

12. The young's modulus of the material of a wire is equal to the ...........(A) stress required to increase its length four times(B) strtess required to prdouce unit strain(C) strain produced in it (D) stress acting on it

13. If x, longitudinal strain is produced in a wire of young's modulus y then energy stroed in the materialof the wire per unit volume is..........

(A) yx2 (B) 2yx2 (C) xy21 2 (D) 2yx

21

14. A steel wire of cross-sectional area 26 m103 can with stand a maximum strain of 10-3 Young's

modulus of steel is .mN102 2

11 The maximum mass the wire can hold is.............

2s

m10g

(A) 40 kg (B) 60 kg (C) 80 kg (D) 100 kg

15. The young's modulus of a rubber string 8 cm long and density 3mkg5.1 is .

mN105 2

8 What will

be the length increase due to its own weight ?

(A) m106.9 5 (B) m106.9 11

(C) m106.9 3 (D) m6.9

16. A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Thenwhat is the stress on B ?(A) Equal to that on A (B) Four times that on A(C) Two times that on A (D) Half that on A

17. If the length of wire is reduced to half then it can hold the .............load.(A) Half (B) Same (C) Double (D) One fourth



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18. There are two wires of same material and same length. While the diameter of second wire is 2 times,the diameter of first wire. Then what will be the ratio of extension produced in the wire by applyingsame load ?(A) 1 : 1 (B) 2 : 1 (C) 1 : 2 (D) 4 : 1

19. When the length of a wire having cross-section area 26 m10 is stretched by 0.1% then tension init is 100 N. Young's modulus of material of wire is...........

(A) 212

mN10 (B) 2

2

mN10 (C) 2

10

mN10 (D) 2

11

mN10

20. Two wires of equal lengths are made of the same material wire A has a diameter that is twice as thatof wire B. If identical weights are suspended from the ends of these wires the increase in lengthis............(A) Four times for wire A as for wire B. (B) Twice for wire A as for wire B.(C) Half for wire A as for wire B. (D) One-fourth for wire A as for wire B.

21. Steel and copper wires of same length are stretched by the same weight one after the other. Young'smodulus of steel the ratio increase in length ?

(A) 52

(B) 53

(C) 45

(D) 25

22. An area of a cross-section of rubber string is 2 cm3. Its length is doubled when stretched with alinear force of 5102 dynes. What will be young's modulus of the rubber in dynes ?

(A) 5104 (B) 5101 (C) 5102 (D) 4101

23. A substance breaks down by a stress of If the density of the material of the wire is then the length ofwire of the substance which will break under its own weight when suspended vertically is.............(A) 66.6 m (B) 60.0 m (C) 33.3 m (D) 30.0 m

24. The temperature of a wire of length 1 meter and area of cross-sectional section 1 cm2 is increasedfrom to If the rod is not allowed to increase in length. What will be the force required ?

211o5

mN10Y,C/10

(A) 103 N (B) 104 N (C) 105 N (D) 109 N25. If longitudinal strain for a wire is 0.03 and its poisson's ratio is 0.5, then what is its lateral strain ?

(A) 0.003 (B) 0.0075 (C) 0.015 (D) 0.4

26. An aluminium rod (Young's modulus 29

mN107 ) has a breaking strain of 0.2 % what is the

minimum cross-sectional area of the rod in order to support a load of 104 Newtons ?

(A) 22 m101 (B) 23 m104.1

(C) 23 m105.3 (D) 24 m101.7



210

27. Two wires of copper having the length in the ratio 4 : 1 and their are as 1 : 4 are stretched by thesame force. What will be the ratio of longitudinal strain in the two wires ?(A) 1 : 16 (B) 16 : 1 (C) 1 : 64 (D) 64 : 1

28. A wire elongates by 1 mm when a load W is hanged from it. If the wire goes ever a pulley and twoweight W each are hang at the two ends. What will be the elongation of the wire ? (in mm)

(A) 2 (B) zero (C) 2

(D)

29. 200 kg weight hanged at a free edge of vertical wire of length 600.5 cm when removed the weight,length reduced by 0.5 cm and it gets original status then what is the young moduluse of wire ?(A) 2.35 1012 N/m2 (B) 1.35 1010 N/m2

(C) 13.5 1011 N/m2 (D) 23.5 109 N/m2

30. The ratio of diameter of two wires of same material is n : 1 the length of wires are 4 m each. Onapplying the same load. What will be the increase in length of their wire ?(A) n2 times (B) n times (C) 2n times (D) None of the above

31. Longitudinal stress of 2mmN1 is applied on a wire what is the % increase in length ?

2

4

mN10Y

(A) 0.002 (B) 0.001 (C) 0.003 (D) 0.0132. A steel wire is stretched with a definate load of If the young's modulus of the wire is Y. For decreasing

the value of Y............(A) Radius is to be decreased (B) Radius is to be increased(C) Length is to be increased (D) None of the above

33. The area of cross-section of a steel wire is

2

11

mN102Y is 0.1 cm2, what will be the force

required to double its length ?

(A) N102 12 (B) N102 11 (C) N102 10 (D) N102 6

34. Two wires A & B are of same materials. Their lengths in the ratio 1 : 2 and diameters are in the ratio2 : 1 when stretched by force BA FandF respectively, they get equal increase in lengths Then the

ratio FBFA

should be...........

(A) 1 : 2 (B) 1 : 1 (C) 2 : 1 (D) 8 : 1

35. The mean distance between the atoms of iron is 10103 and interatomic force constant for iron is

mN7 . What is the young's modulus of elasticity for iron ?

(A) 25

mN1033.2 (B) 2

10

mN103.23

(C) 210

mN10233 (D) 2

10

mN1033.2



211

36. A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section22 cm10 , the other end of the wire is rigidly fixed. If of linear expansion of the wire

C/108 o6 and young's modulus 211

mN102.2Y and its temperature is increased by

50C then the increase in the tension of the wire will be..........(A) 4.2 N (B) 4.4 N (C) 2.4 N (D) 8.8 N

37. A uniform plank of young's modulus Y is moved over a smooth horizontal surface by a constanthorizontal force F, The area of cross-section of the plank is A. What is the compressive strain on itsplank in the direction by the force ?

(A) AYF

(B) AYF2

(C)

AYF

21

(D) AYF3

38. The length of a wire is 1.0 m and the area of cross-section is 22 cm100.1 . If the work done forincrease in length by 0.2 cm is 0.4 joule. Then what is the young's modulus ? Of material of the wire?

(A) 210

mN100.2 (B) 2

10

mN100.4

(C) 211

mN100.2 (D) 2

11

mN100.4

39. A rubber cord catapult has cross-sectional area 25 mm2 and initial length of cord is 10 cm. It isstretched to 5 cm and then released to project a missile of mass 5 gm. Taking

28

rubber mN105Y velocity of projected missile is............

(A) sm20 (B) 1s

m100 (C) 1sm250 (D) 1s

m200

40. A wire of cross-section 4 mm2 is stretched by 0.1 mm by a certain weight. How far (length) will bewire of same material and length but of area 8 mm2 stretched under the action of same force.(A) 0.05 mm (B) 0.10 mm (C) 0.15 mm (D) 0.20 mm

41. According to Hooke's law of elasticity stress is increased the ratio of stress toi strain.........(A) increases (B) Decreases(C) becomes zero (D) Remains constant

42. Young's modulus of rubber is 24

mN10 and area of cross section is 2 cm2 if force of 5102 dyne is

applied along its length then its initial length L becomes .............(A) 3L (B) 4L(C) 2L (D) None of the above



212

43. A copper wire of length 4 m and area of cross-section 1.2 cm2 is stretched with a force of 3108.4 N.

If young's modulus for copper is 211

mN102.1 What will be the length increase of the wire ?

(A) 1.33 mm (B) 1.33 cm (C) 2.66 mm (D) 2.66 cm

44. If the interatomic spacing in a steel wire is &A3 o .mN1020Y 2

10Steel the force constant =

.............

(A) AN106 2 (B) A

N106 9 (C) AN106 5 (D) A

N106 5

45. A wire of length 2 m is made from 10cm3 of copper. A force F is applied so that its length increasesby 2mm. Another wire of length 8 m is made from the same volume of copper. If the force F isapplied to it, its length will increase by............(A) 0.8 cm (B) 1.6 cm (C) 2.4 cm (D) 3.2 cm

46. A wire of length L and radius r is rigidly fixed at one end on stretching the other end of the wire aforce F the increase in its lengths is L. If another wire of same material but of length 2L and radius 2ris stretched with a force of 2F, the increase in its length will be ..........

(A) (B) 2 (C) 2

(D) 4

47. In steel the young's modulus and the strain at the breaking point are 211

mN102 and 0.15

respectively the stress at the breaking point for steel is therefore ...........

(A) 211

mN1033.1 (B) 2

12

mN1033.1

(C) 213

mN105.7 (D) 2

10

mN103

48. Which of the following statement is correct(A) Hooke's law is applicable only within elastic limit.(B) The adiabatic and isothermal elastic constants of a gas area equal.(C) Young's modulus is dimensionsless.(D) Stress multiplied by strain is equal to stored energy.

49. The force required to stretch a steel wire of 2cm1 cross-section to 1.1 times its length would be

2

11

mN102Y

(A) N102 6 (B) N102 3 (C) N102 6 (D) N102 7



213

50. Which one of the following quantities does not have unit of force per unit area..........(A) stress (B) strain(C) Young's modulus of elasticity (D) pressure

51. A copper wire and a steel wire of same diameter and length are connected end to end a force isapplied, which stretches their combined length by 1 cm, the two wires will have.......(A) different stresses and strains (B) the same stress and strain(C) the same strain but different stresses (D) the same stress but different strains

52. A steel ring of radius r and cross-section area 'A' is fitted on to a wooden disc of radius R(R > r ) If young's modulus be E then what is force with which the steel ring is expanded ?

(A) rRAE (B)

rrRAE (C)

E R rA R

(D) AREr

53. A wire of diameter 1 mm breaks under a tension of 100 N. Another wire of same material as that ofthe first one, but of diameter 2 mm breaks under a tension of.........(A) 500 N (B) 1000 N (C) 10,000 N (D) 4000 N

54. A fixed volume of iron is drawn into a wire of length L. The extension x produced in this wire be aconstant force F is propotional to..........

(A) 2L1

(B) L1

(C) L2 (D) L

55. On applying a stress of 28

mN1020 the length of a perfect elastic wire is doubled. What will be its

Young's modulus ?

(A) 28

mN1040 (B) 2

8

mN1020

(C) 28

mN1010 (D) 2

8

mN105

56. To keep constant time, watches are fitted with balance wheel made of........(A) invar (B) stainless steel (C) Tungsten (D) platinum

57. A wire is stretched by 0.01 m by a certain force F. Another wire of same material whose diameterand length are double to the original wire is stretched by the same force ? Then what will be itselongation ?(A) 0.005 m (B) 0.01 m (C) 0.02 m (D) 0.002 m

58. The Coefficient of linear expansion of brass & steel are 21 & If we take a brass rod of length 1& steel rod of length 2 at C0o , their difference in length 12 will remain the same at atemperature if.................

(A) 1221 (B) 1212

(C) 2221

22 (D) 2211



214

59. A rod is fixed between two points at C20 o The Coefficient of linear expansion of material of rad is

C/101.1 o5 and Young's modulus is 211

mN102.1 . Find the stress developed in the rod if

temperature of rod becomes C10 o .

(A) 27

mN1032.1 (B) 2

15

mN1010.1 (C) 2

8

mN1032.1 (D) 2

6

mN1010.1

60. How much force is required to produce an increase of 0.2% in the length of a bross wire of diameter

0.6 mm (Young's modulus for brass 211

mN109.0 ).

(A) Nearly 17 N (B) Nearly 34 N (C) Nearly 51 N (D) Nearly 68 N

61. A 5m long aluminium wire

2

10

mN107Y of diameter 3mm supports a 40 kg mass. In order

to have the same elongation in a copper wire 210

mN1012Y of the same length under the same

weight, the diameter should now be in mm............(A) 1.75 (B) 1.5 (C) 2.5 (D) 5.0

62. Two similar wires under the same load yield elongation of 0.1 mm and 0.05 mm respectively. If thearea of Cross - section of the first wire is 4mm2. Then what is the area of cross - section of thesecond wire ?

(A) 2mm6 (B) 2mm8 (C) 2mm10 (D) 2mm12

63. An iron rod of length 2m and cross-section area of 2mm50 stretched by 0.5 mm, when a mass of250 kg is hung from its lower end. What is young's modulus of the iron rod ?

(A) 210

mN106.19 (B) 2

15

mN106.19

(C) 218

mN106.19 (D) 2

20

mN106.19

64. A load W produces an extension of 1mm in a thread of radius r. Now if the load is made 4 w andradius is made 2r all other things remaining same the extension will becomes..............(A) 4 mm (B) 16 mm (C) 1 mm (D) 0.25 mm

65. A steel wire of 1m long and 2mm1 cross sectional area is hung from rigid end when weight of 1 kg

is hung from it then change in length will be............

2

11

mN102Y

(A) 0.5 mm (B) 0.25 mm (C) 0.05 mm (D) 5 mm



215

66. Calculate the work done, if wire is loaded by 'M g' weight and the increase in length is 'l' ?

(A) mgl (B) Zero (C)mg

(D) 2mgl

67. Two wires of same diameter of the same material having the length and 2 . If the force F isapplied on each, what will be the ratio of the work done in the two wires ?(A) 1 : 2 (B) 1 : 4 (C) 2 : 1 (D) 1 : 1

68. A 5 meter long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 meterabove the four. The wire was elongated by 1 mm. What is the stored in the wire due to stretching ?(A) Zero (B) 0.05 Joule(C) 100 Joule (D) 500 Joule

69. If the force constant of a wire is k. What is the work done in increasing the length of the wire by ?

(A) 2k

(B) k (C)2

k 2(D) 2k

70. Wire A and B are made from the same material. A has twice the diameter and three times the lengthof B. If the elastic limits are not reached when each is stretched by the same tension, what is the ratioof energy stored in A to that in B ?(A) 2 : 3 (B) 3 : 4 (C) 3 : 2 (D) 6 : 1

71. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to thelower and. The weight stretches the wire by 1 mm. Then what is the elastic energy stored in the wire?(A) 0.1 J (B) 0.2 J (C) 10 J (D) 20 J

72. A brass rod of cross sectional area 1 cm2 and length 0.2 m is compressed length wise by a weight of

5 kg. If young's modulus of elasticity of brass is 211

mN101 and 2s

m10g Then what will be

increase in the energy of rod ?

(A) J10 5 (B) J105.2 5 (C) J105 5 (D) J105.2 4

73. Young's modulus of the material of a wire is Y. On pulling the wire by a force F the increase in itslength is x, what is the potential energy of the stretched wire ?

(A) Fx21

(B) Yx21

(C) 2Fx21

(D) None of these

74. The work per unit volume to stretch the length by 1% of a wire with cross - sectional area 1 mm2 will

be............

2

11

mN109Y

(A) J109 11 (B) J105.4 7 (C) J109 7 (D) J105.4 11



216

75. A wire of length 50 cm and cross - sectional area of 1 mm2 is extended by 1mm what will be the

required work ? 211 Nm102Y

(A) J106 2 (B) J102 2 (C) J104 2 (D) J101 2

76. If a spring extends by x cm loading then what is the energy stored by the spring ? (If T is tension inthe spring & K is spring constant)

(A)x2

T2

(B)k2

T2

(C) 2Tx2

(D)kT2 2

77. On stretching a wire what is the elastic energy stored per unit volume ?

(A)F

2AL (B) L2FA

(C) A2FL

(D) 2FL

78. When a force is applied on a wire of uniform cross-sectional area 26 m103 and length 4m, the

increase in length is 1 mm. what will be energy stored in it ?

2

11

mN102Y

(A) 62. 50 J (B) 0.177 J (C) 0.075 J (D) 0.150 J79. k is the force constant of a spring what will be the work done in increasing its extension form

1 to 2 be ?

(A) 1 2k (B) 122k (C) 2

12

2k (D) 21

222

k

80. When a 4 kg mass is hung vertically on a light spring that obeys Hook's law, the spring stretches by2 cm what will be the work required to be done by an external agent in stretching this spring by5 cm ?(A) 4.900 Joule (B) 2.450 Joule (C) 0.495 Joule (D) 0.245 Joule

81. The isothermal elasticity of a gas is equal to....................(A) Density (B) Volume (C) Pressure (D) Specific heat

82. If the volume of a block of aluminium is decreased, by the pressure (stress) on its surface is increased

by.................(Bulk modulus of 210 Nm105.7A )

(A) 210

mN105.7 (B) 2

8

mN105.7 (C) 2

6

mN105.7 (D) 2

4

mN105.7

83. The specific heat at constant pressure and at constant volume for an ideal gas are vp CandC and

isothermal elasticities are EandE respectively. What is the ratio of EandE .

(A)p

v

CC

(B)v

p

CC

(C) vp CC (D)vp CC

1



217

84. What is the ratio of the adiabatic to isothermal elasticities of a triatomic gas ?

(A) 43

(B) 34

(C) 1 (D) 35

85. To what depth below the surface of sea should a rubber ball be taken as to decrease its volume by

0.1% (Take : density of sea water 3mkg1000 Bulk modulus of rubber 2

8

mN109 ,acceleration

due to gravity 2sm10 )

(A) 9 m (B) 18 m (C) 180 m (D) 90 m

86. The compressibility of water 5104 per unit atmospheric pressure. The decrease in volume of100 cubic centimeter of water under a pressure of 100 atmosphere will be................

(A) CC104 5 (B) CC104 5 (C) 0.025 CC (D) 0.004 CC

87. If a rubber ball is taken at the depth of 200m in a pool, Its volume decreases by 0.1% . If the density

of the water is 233

sm10g&

mkg101 . Then waht will be the volume elasticity in ?

mN

2

(A) 810 (B) 8102 (C) 910 (D) 9102

88. For a constant hydraulic stress on an object, the fractional change in the object volume

and

its bulk modulus (B) are related as...............(A) 0.01 (B) 0.06 (C) 0.02 (D) 0.03

89. When a pressure of 100 atmosphere is applied on a spherical ball then its volume reduces to 0.01%

What is the bulk moduls of the material of the rubber in 2cmdyne .

(A) 121010 (B) 12101 (C) 1210100 (D) 121020

90. The pressure applied from all directions on a cube is p. How much its temperature should be raisedto maintain the orginal volume ? The volume elasticity. of the cube is B and the coefficient of volumeexpansion is .

(A) P

(B) P

(C)p

(D) p

91. A uniform cube is subjected to volume compression. If each side is decreased by 1% Then what isbulk strain ?(A) 0.01 (B) 0.06 (C) 0.02 (D) 0.03



218

92. The ratio of two specific heats of gas v

p

CC

for Argon is 1.6 and for hydrogen is 1.4. Adiabatic

elasticity of Argon at pressure p is E. Adiabatic elasticity of hydrogen will also be equal to E at thepressure.

(A) p (B) P87

(C) P78

(D) 1.4 P

93. What is the isothermal bulk modulus of a gas at atmospheric pressure ?(A) 1 mm of Hg (B) 13.6 mm of Hg

(C) 25

mN10013.1 (D) 2

5

mN10026.2

94. The bulk modulus of an ideal gas at constant temperature.........(A) is equal to its volume V (B) is equal to P/2(C) is equal to its pressure P (D) cannot be determined

95. A material has poisson's ratio 0.50. If uniform rod of it suffers a longitudinal strain of 3102 . Thenwhat is percentage change in volume ?(A) 0.6 (B) 0.4 (C) 0.2 (D) 0

96. There is no change in the volume of a wire due to change in its length on stretching. What is thepossion's ratio of the material of the wire....(A) +0.5 (B) -0.50 (C) 0.25 (D) -0.25

97. Which statement is true for a metal......

(A) Y (B) Y (C) Y (D) 1Yη

98. Which of the following relation is true

(A) 61kY3 (B) nygnyk

(C) Ynk66 (D) nnY5.06

99. Two wires A & B of same length and of the same material have the respective radius r, & r2 their oneend is fixed with a rigid support and at the other end equal twisting couple is applied. Then what willwe be the ratio of the angle of twist at the end of A and the angle of twist at the end of B.

(A) 22

21

rr

(B) 21

22

rr

(C) 41

42

rr

(D) 42

41

rr

100. The poisson's ratio can not have the value...........(A) 0.7 (B) 0.2 (C) 0.1 (D) 0.5



219

101. The value of poisson's ratio lies between........

(A) 21to1 (B) 2

1to43

(C) 1to21

(D) 1 to 2

102. If the young's modulus of the material is 3 times its modulus of rigidity. Then what will be its volumeelasticity ?

(A) zero (B) infinity (C) 210

mN102 (D) 2

10

mN103

103. For a given material the Young's modulus is 2.4 times that of rigidity modulus. What is its poisson'sratio ?(A) 2.4 (B) 1.2 (C) 0.4 (D) 0.2

104. The lower surface of a cube is fixed. On its upper surface is applied at an angle of 300 from itssurface. What will be the change of the type ?(A) shape (B) size (C) none (D) shape & size

105. The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twistedthrough an angle of 300. Then what is the angle of shear ?(A) 120 (B) 0.120 (C) 1.20 (D) 0.0120

106. Mark the wrong statement.(A) Sliding of moleculawr layer is much easier than compression or expansion.(B) Receiprocal of bulk modulus is called compressibility.(C) Twist is difficult in big rod as compared to small rod.(D) Which is more strong out of hollow and solid cylinder having equal length and mass ?

107. A 2m long rod of radius 1 cm which is fixed from one end is gien a twist of 0.8 radians. What will bethe shear strain developed ?(A) 0.002 (B) 0.004 (C) 0.008 (D) 0.016

108. Shearing stress causes change in(A) length (B) breadth (C) shape (D) volume

109. What is the relationship between Young's modulus Y, Bulk modulus k and modulus of rigidity ?

(A) k3k9Y

(B) k3yky9Y

(C) k3

k9Y

(D) k9k3Y

110. What is the possible value of posson's ratio ?(A) 1 (B) 0.9 (C) 0.8 (D) 0.4

111. The graph shown was obtained from experimentalmeasurements of the period of oscillations T for differentmasses M placed in the scale pan on the lower end of thepassing through the origin is that the......(A) Spring did not obey Hooke's law(B) Amplitude of the oscillations was large(C) Clock used needed regulating(D) Mass of the pan was neglected



220

112. A graph is shown between stress and strainfor metals. The part in which Hooke's lawholds good is(A) OA (B) AB(C) BC (D) CD

113. The strain-stress curves of three wires of different materialsare shown in the figure. P, Q and R the elastic limits of thewires the figure shows that(A) Elasticity of wire P is maximum.(B) Elasticity of wire Q is maximum.(C) Tensile strength of R is maximum(D) none of above

114. The diagram shows a force extension graph for a Rubberband consider the following statements.(I) It will be easier to compress these

rubber than expand it.(II) Rubber does not return to its original

length after it is stretched.(III) The rubber band will get heated if it

is stretched and relased.Which of these can be deduced from the graph.(A) III only (B) II and III (C) I and III (D) I only

115. The stress versus strain graph for wires of two material A& B are as shown in the figure. If YA & YB are the young'smodulus of the materials then(A) YB = 2YA

(B) YA = YB

(C) YB = 3YA

(D) YA = 3YB

116. The load versus elongation graph for four wires of the samematerial is shown in the figure. The thickest wire isrepresented by the line.(A) OD (B) OC(C) OB (D) OA



221

117. The adjacent graph shows the extension of a wire of length1m suspended from the top of a roof at one end with theload W connected to the other end. If the cross sectionalarea of the wire is 10-6 m2, calculate the young's modulusof the material of the wire.

(A) 211

mN102 (B) 2

11

mN102

(C) 212

mN103 (D) 2

12

mN102

118. The graph is drawn between the applied force F and thestrain (x) for a thin uniform wire the wire behaves as aliquid in the part.(A) ab (B) bc(C) cd (D) oa

119. The graph shows the behaviour of a length of wire in theregion for which the substance obey's Hooke's law. P &Q represent.(A) p = applied force, Q = extension(B) p = extension, Q = applied force(C) p = extension, Q = stored elastic energy(D) p = stored elastic energy, Q = extension

120. The potential energy U between two nmolecules as afunction of the distance x between them has been shownin the figure. The two molecules are.(A) Attracted when x lies between A & B

and are repelled when x lies between B & C.(B) Attracted when x lies between B and

C and are repelled when x lies between A and B.(C) Attracted when they reach B.(D) Repelled when they reach B.

121. The value of force constant between the applied elasticforce F and displacement will be

(A) 3 (B) 31

(C) 21

(D)23



222

122. The diagram shows stress v/s strain curvefor the materials A and B. From the curveswe infer that(A) A is brittle but B is ductile(B) A is ductile and B is brittle(C) Both A & B are ductile(D) Both A & B are brittle

123. Which are of the following is the young'smodulus (in N/m2) for the wire having thestress strain curve in the figure.

(A) 111024

(B) 11100.8

(C) 111010

(D) 11100.2

124. The diagram shows the change x in thelength of a thin uniform wire caused by theapplication of stress F at two differenttemperature T1 & T2. The variation

(A) 21 TT

(B) 21 TT

(C) 21 TT

(D) None of these

125. The point of maximum and minimumattraction in the curve between potentialenergy (U) and distawnce (r) of a diatomicmolecules are respectively.(A) S and R (B) T and S(C) R and S (D) S and T

Assertion and Reason :Read the assertion and reason carefully to mark the correct option out of the option given below(A) If both assertion and reason are true and reason is the correct explanation of the assertion.(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.(C) If assertion is true but reason is false.(D) If assertion and reason both are false.



223

126. Assertion : The stretching of a coil is determined by its shear modulus.Reason : Shear modulus change only shape of a body keeping its dimensions unchanged.(A) a (B) b (C) c (D) d

127. Assertion : The bridges are declared unsafe after a long use.Reason : Elastic strength of bridges decrease with(A) a (B) b (C) c (D) d

128. Assertion : Two identical solid balls, one of ivory and the other of wet clay are dropped from thesame height on the floor. Both the balls will rise to same height after.Reason : Ivory and wet-clay have same elasticity.(A) a (B) b (C) c (D) d

129. Assertion : Young's modulus for a perfectly plastic body is zero.Reason : For a perfectly plastic body is zero.(A) a (B) b (C) c (D) d

130. Assertion : Identical spring of steel and copper are equally stretched more will be done on the steelspring.Reason : Steel is more elastic than copper.(A) a (B) b (C) c (D) d

131. A wire is stretched to double the length which of the following is false in this context ?(A) Its volume increased (B) Its longitudinal strain is I(C) Stress = Young's modlus (D) Stress = 2x Young's modulus

132. Which is the dimensional formula for modulus of rigidity ?

(A) 211 TLM (B) 211 TLM (C) 121 TLM (D) 221 TLM

133. When more than 20 kg mass is tied to the end of wire it breaks what is maximum mass that can betied to the end of a wire of same material with half the radius ?(A) 20 kg (B) 5 kg (C) 80 kg (D) 160 kg

134. When 100 N tensile force is applied to a rod of 10-6 m2 cross-sectional area, its length increases by1% so young's modulus of material is..........(A) 1012 Pa (B) 1011 Pa (C) 1010 Pa (D) 102 Pa

135. A composite wire is made by joining ends of two wires of equal dimensions, one of copper and theother of steel. When a weight is sttached to its end the ratio of increase in their length is .........

CopperSteel Y720Y

(A) 20.7 (B) 10.7 (C) 7:20 (D) 1:7136. A rubber ball when taken to the bottom of a 100 m deep take decrease in volume by 1% Hence, the

bulk modulus of rubber is............

2s

m10g

(A) 106 Pa (B) 108 Pa (C) 107 Pa (D) 109 Pa



224

137. Young's modulus of a rigid body is(A) 0 (B) 1 (C) (D) 0.5

138. Pressure on an object increases from .Pa10165.1toPa1001.1 55 He volume decrease by10% at constant temperature. Bulk modulus of material is........

(A) Pa1055.1 5 (B) Pa102.51 5

(C) Pa104.102 5 (D) Pa108.204 5

139. Cross-sectional area oif wire of length L is A. Young's modulus of material is Y. If this wire acts as aspring what is the value of force constant ?

(A) LYA

(B) L2YA

(C) LYA2

(D) AYL

Surface Tension140. Writing on black board with a pieace of chalk is possible by the property of

(A) Adhesive force (B) Cohesive force (C) Surface force (D) Viscosity

141. When there is no external force, the shape of liquid drop is determined by

(A) Surface tension of liquid (B) Density of Liquid

(C) Viscosity of liquid (D) Tempreture of air only

142. Soap helps in cleaning because

(A) chemicals of soap change

(B) It increase the surface tension of the soluiton.

(C) It absorbs the dirt.

(D) It lowers the surface tension of the solution

143. A beaker of radius 15 cm is filled with liquid of surface tension 0.075 N/m. Force across an imaginarydiameter on the surface ofliquid is

(A) 0.075 N (B) N105.1 2

(C) 0.225 N (D) N1025.2 2

144. A square frame of side L is dipped in a liquid on taking out a membrance is fomed if the surfacetension of the liquid is T, the force acting on the frame will be.

(A) 2 TL (B) 4 TL (C) 8 TL (D) 10 TL

145. The force required to separate two glass plates of area 10-2 m2 with a film of water 0.05 mm thick

between them is (surface tension of water is mN1070 3 )

(A) 28 N (B) 14 N (C) 50 N (D) 38 N



225

146. Surface tension of a liquid is found to be infuenced by

(A) It increases with the increase of temprature.

(B) Nature of the liquid in contact.

(C) Presense of soap that increaase it.

(D) Its variation with the concentration of the liquid.

147. A thm metal disc of radius r floats on water surface B and bends the surface down wards along theperimeter making an angle Q with vertical edge of the disc. If the disc displaces a weight of water Wand surface tension of water is T, then the weight at metal dis

(A) wrT2 (B) wcosrT2

(C) wcosrT2 (D) cosrT2w148. A thin liquid film formed between a u-shaped wire and

a light slider supports a weight of N105.1 2 (seefigure). The length of the slider is 30 cm and its weightnegligible. The surface tension of the liquid film is.

(A) 1mN0125.0 (B) 1mN1.0

(C) 1mN05.0 (D) 1mN025.0

Surface Energy149. Radius of a soap bubble is 'r', surface tension of soap solution is T. Then without incresing the

temprature how much energy will be needed to double its radius.

(A) Tr4 2 (B) Tr2 2

(C) Tr12 2 (D) Tr24 2

150. The amount of work done in blowing a soap bubble such that its diameter increases from d to D is(T = Surface tension of solution)

(A) TdD4 22 (B) TdD8 22

(C) TdD 22 (D) TdD2 22

151. A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions if theT is the surface tension of soap solution the energy spent in the slowing is.

(A) 2Tr3 (B) 2Tr6 (C) 2Tr12 (D) 2Tr24152. The surface tension of a liquid is 5 N/m. If a thin film of the area 0.02 m2 is formed on a loop, then

its surface energy will be

(A) J105 2 (B) J105.2 2 (C) J102 1 (D) J105 1



226

153. A frame made of a metalic wire enclosing O surface area A is covered with a soap film. If the areaof the frame metalic wire is reduced by 50% the energy of the soap film will be changed by(A) 100% (B) 75% (C) 50% (D) 25%

154. Two small drops mercury, each of radius R, coaless the form a single large drop. The ratio of thetotal surface energies before and after the change is.

(A) 21

2:1 (B) 1:221

(C) 2 : 1 (D) 1 : 2

155. The work done is blowing a soap bubble of 10 cm radius is

(surface tension od the soap solution is m/N100

3)

(A) Joule1036.75 4 (B) Joule1068.37 4

(C) Joule1072.150 4 (D) Joule36.75

156. The work done increasing the size of a soap film drom cm11cm10 is Joule103 4 . Thesurface tension of the film is

(A) mN105.1 2 (B) m

N100.3 2 (C) mN100.6 2 (D) m

N100.11 2

157. A big drop of radius R is formed by 1000 small droplets of coater then the radius of small drop is

(A) 2R

(B) 5R

(C) 6R

(D) 10R

158. 8000 identioal water drops are combined to form a bigdrop. Then the ration of the final surfaceenergy to the intilial surface energy of all the drops together is(A) 1 : 10 (B) 1 : 15 (C) 1 : 20 (D) 1 : 25

159. The relation between surface tension T. Surface area A and surface energy E is given by.

(A) AET (B) EAT (C) A

TE (D) EAT

Angle of Contact160. If a coater drop is kept between two glasses plates then its shape is

(A) (B) (C)

(D) None of these



227

161. A liquid wets a solid completely. The menisions of the liquid in a surfficently long tube is(A) Flat (B) Concave (C) Convex (D) Cylindrical

Pressure Difference162. When two soap bubbles of radius r1 and r2 (r2 > r1) coalesce, the radius of curvature of common

surface is...........

(A) 12 rr (B)21

12

rrrr

(C)12

21

rrrr (D) 12 rr

163. The excess of pressure inside a soap bubble than that of the other pressure is

(A) rT2

(B) rT4

(C) r2T

(D) rT

164. The radill of two soap bubbles are r1 and r2. In isothermal conditions two meet together is vacumThen the radius of the resultant bubble is given by

(A) 2/rrR 21 (B) 3211 rrrrR

(C) 22

21

2 rrR (D) 21 rrR

165. A spherical drop of coater has radius 1 mm if surface tension of contex is m/N1070 3 differenceof pressures between inside and outside of the spherical drop is

(A) 2mN35 (B) 2m

N70 (C) 2mN140 (D) zero

166. In capilley pressure below the curved surface at water will be(A) Equal to atomospheric (B) Equal to upper side pressure(C) More than upper side pressure (D) Lesser than upper side pressure

167. Two bubbles A and B (A>B) are joined through a narrow tube than(A) The size of a will increase(B) The size of B will increase(C) The size of B will increase untill thenpressure equals(D) None of these

168. If the excess pressure inside a soap bubble is balanced by oil column of height 2 mm then the surfacetension of soap solution will be.Cr = 1 and density d = 0.8 gm/cc)

(A) mN9.3 (B) m

N109.3 2 (C) mN109.3 3 (D) m

N109.3 1

Capillarity169. A capillary tube at radius R is immersed in water and water rises in it to a height H. Mass of water

in the capillary tube is M. If the radius of the tube is doubled. Mass of water that will rise in thecapillary tube will now be(A) M (B) 2M (C) (D) 4M



228

170. A vesel whose bottom has round holes with diametre of 0.1 mm is filled with water. The maximumheight to which the water can be filled without leakage is

(S.T. of water = cmdyne75

2sm1000g )

(A) 100 cm (B) 75 cm (C) 50 cm (D) 30 cm171. The correct relation is

(A) hdgcosT2r

(B)

cosT2

hdgr (C)

cos

dghT2r (D) hdg2cosTr

172. In a capillary tube water rises by 1.2 mm. The height of water that will rise in another capillary tubehaving half the radius of the first is(A) 1.2 mm (B) 2.4 mm (C) 0.6 mm (D) 0.4 mm

173. Water rises in a vertical capillary tube upto a beight of 2.0 cm. If tube is inclined at an angle of 600

with the vertical then the what length the water will rise in the tube.

(A) 2.0 cm (B) 4.0 cm (C) cm3

4(D) cm22

174. The lower end of a glass capillary tube is dipped in water rises to a height of 8 cm the tube is thenbroken at a height of 6 cm. The height of water column and engled as contact will be

(A) 1 36 cm . sin4

(B) 1 46 cm . sin5

(C) 43cos.cm6 1 (D) 1 16 cm . sin

2

175. A large number of water drops each of rdius r combine to have a drop of radius R. If the surfacetension is T and the mechanical equllvalent at heat is J then the rise in tempreature will be

(A) rJT2

(B) RJT3

(C)

R1

r1

JJ3

(D)

R1

r1

JT2

Caraphical Question176. The correct curve between the height or depression h of liquid in a capillary tube and its radius is



229

177. A soap bubble is blown with the help of a mechanical pump at the mouth-of a tube the pumpproduces a certion increase per minit in the volume of the bubble irrespective of its internal pressurethe graph between the pressure inside the soap bubble and time t will be

178. Which graph present the variation of surface tension with temperature over small temperature rangesfor coater.

Comprehension type questionPassage - I

When liquid medicine of desting S is to be put in the eye. It is done with the help of a dropperas the bulb on the top of the dropper is pressed a drop forms at the opening od the dropper we wishto estimate the size of the drop. We dirst assume that the drop formed at the opening is sphericalbecause the requires a minimum increase in its surface energy. To determine the size we calculate thenet vertical force due to surface tension T when the radius od the drop is R. When this forcebecomes smaller than the weight of the drop the drop gets detched from the dropper.

179. If the radius od the opening od the dropper is r ; the vertical force due to the surface tension on thedrop of radius R. (cassuming r << R) is

(A) Tr2 (B) TR2 (C)R

Tr2 2(D)

rTR2 2

180. If 2334 ms10mkg10,m105 T = 0.11 N m-1 the radius of the drop when itdetaches from the dropper is approximately

(A) m104.1 3 (B) m103.3 3 (C) m100.2 3 (D) m101.4 3



230

181. After the drop detaches its surface energy is

(A) J104.1 6 (B) J107.2 6 (C) J104.5 6 (D) J101.8 6

Assertion & Reason type questionsRead the assertion and reason carefully and mark the correct option given below.(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.(c) If assertion is true but reason is false.(d) If the assertion and reason both are false.

182. Assertion : It is better to wash the clothes in cold soap solution.Reason : The surface tension of cold solution is more then the surface tension of hot solution.(A) a (B) b (C) c (D) d

183. Assertion : When height of a tube is less then liquid rise in the capillary tube the liquid does notovertow.Reason : Product of radius of meniscus and height of liquid incapilling tube always remains constant.(A) a (B) b (C) c (D) d

184. Assertion : The impurities always decrease the surface tension of a liquid.Reason : The change in surface tension of the liquid depends upon the degree of cont amination ofthe impurity.(A) a (B) b (C) c (D) d

185. Assertion : The concept of surface tension is help only for liquids.Reason : Surface tension does not hold for gases.(A) a (B) b (C) c (D) d

186. Assertion : The water rises higher in a capillary tube of small diametre than in the capillary tube oflarge diamtre.Reason : Height through which liquid rises in a capillay tube is inversely proportional to the diameterof the capillary tube.(A) a (B) b (C) c (D) d

187. Assertion : Tiny drops of liquid resist deforming forces better than bigger drops.Reason : Excess pressure inside a drop is directly proportional to surface tension.(A) a (B) b (C) c (D) d

Pressure and Density188. When a large bubble rises drom the bottom of a lake to the surface. Its radius double S. It atmospheric

pressure in euqal to that of colurnn of colurnn of water height H then the depth of Lake is(A) H (B) 2H (C) 7H (D) 8H



231

189. A trangular lamind of area A and, height h is immersed in a liquid of density S in a vertical plane withits base on the surface of the liquid. The thrust on lamina is

(A) ghA21

(B) ghA31

(C) ghA61

(D) ghA32

190. The density S of coater of bulk modulus B at a depth y in the ocean is related to the density atsurface so by the relation.

(A)

Bgy1 0

0 (B)

Bgy1 0

0

(C)

Bgyh1 0

0 (D)

gy

B10

0

191. By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density

3cmgm6.13 ) using the straw, he can drink water from a glass up to a maximum depth of

(A) 10 cm (B) 75 cm (C) 13.6 cm (D) 1.36 cm192. The pressure on a swimmer 20 m below the surface of coater at sea level is

(A) 1.0 atm (B) 2.0 atm (C) 2.5 atm (D) 3.0 atm

Pascal's Law and Archimedes Principal193. A spherical solid ball of volume V is made of a material of density S. It is falling through a liquid of

density S2 (S2 < S1). Assume that the liquid opplies a viscous force on the ball that is proportional tosquare of its speed V. i.e. Fviscous = - KV2 (K > 0) The terminal speed of the ball is

(A)vg

K (B)

vgK

(C) 1 2gvK

(D) 1 2gv

K

194. The fraction of floating object of volume VO and density do above the surface of a Liquid as densityd will be

(A) dd0 (B)

0

0

dddd (C) d

dd 0(D)

0

0

dddd

195. A body floats in water with one-thired od its volume above the surface of water. It is placed in oil itfloats with half of : Its volume above the surface of the oil. The specific gravity od the oil is.

(A) 35

(B) 34

(C) 23

(D) 1

196. If there were no gravity which of the following will not be there for a fluid.(A) Viscosity (B) Surface tension(C) pressure (D) Archime des's upward thrust



232

197. A piece of solid weighs 120 g in air, 80 g in water and 60 g in liquid the relative density of the solidand that of the solid and that of the liquid are respectively.

(A) 3, 2 (B) 43,2 (C) 2,

43

(D) 23,3

198. Ice pieces are floating in a beaker A containing watre and also in a beakre B containing miscibleliquid of specific gravity 1.2 Ice melts the level of(A) water increases in A (B) water decreases in A(C) Liquid in B decrease B (D) Liquid in B increase

Fluid Flow199. An engine pumps water continuously through a hose water leares the hose with a velocity V and m

is the mass per unit length of the watre Jet what is the rate at which kinetic energy is imperted towater.

(A)3mv

21

(B) 3mv (C) 2mv21

(D) 2vmv21

200. The height of the dam in an hydro electric power station is 10 m. In order to generate 1 MW ofelectric power, the mass of water (in kg) that must full per second on the brades of turbine is(A) 106 (B) 105 (C) 103 (D) 104

201. Eight drops of a liquid of density 3 and each of radius a are fallingt through air with a constantvelocity 3.75 cm S1 when the eight drops coalesce to form a single drop the terminal velocity of thenew drop will be

(A) 12 ms1015 (B) s/m104.2 2 (C) 12 ms1075.0 (D) s/m1025 2

202. A cylinder of height 2.0 m is completely filled with water. The velocity of efflux of water cim m/sthrough a small hole on the side will of the cylinder mear its bottom is(A) 10 (B) 20 (C) 25.5 (D) 5

203. There is a hole in the bottom of tank having water. If total pressure at bottom 3 atm (1 atm ) then thevelocity of water flowig drom hole is

(A) sm400 (B) s

m60 (C) sm600 (D) None of these

204. Two drops of the same radius are falling through air with a steady velocity for 5 cm per sec. If thetwo drops coakesce the terminal velocity would be(A) 10 cm per sec (B) 2.5 cm per sec

(C) secpercm45 31

(D) secpercm25

205. An application of Bernouli's equation for liquid flow is found in(A) Dynamic lift of an aeroplane (B) Viscocity metere(C) Capillary rise (D) tly dulic press



233

206. An L-Sp aped tube with a small office is held in a waterstream as shwon in fig. The upper end of the tube is10.6 cm above the surface of water. What will be theheight of the set of water coming from the office velocityof water stream is 2.45 m/s.(A) zero (B) 20.0 cm(C) 10.6 cm (D) 40 cm

207. A tank is filled with water up to a height H. Water isallowed to come out of a hole P in one of the walls at adepth D below the surface of water express thehorizontal distunce x in terms of H and D.

(A) DHDx (B)

2

DHDx

(C) 2 DHDx (D) DHD4x

208. An incomepressible fluid flows steadily through a cylinderical pipe which has radius 2r at point A andradius r at B further along the flow direction. It the velocity at point A is V, its velocity at point B.

(A) 2v (B) v (C) 2v

(D) 4v

209. If the terminal speed of a sphere of gold

3m

kg5.19density is 2.0 m/s in a viscous liquid

3m

kg5.1density find the terminal speed of a sphere of siher

3m

kg5.10density of the

same size in the same liquid.

(A) sm133.0 (B) s

m2.0 (C) sm1.0 (D) s

m4.0

210. Two solid spheres of same metal but of mass M and 8M full simutineously on a viscous liquid andtheir terminal velocity are V and 'nv' then value of 'n' is(A) 16 (B) 8 (C) 4 (D) 2

211. Two metal Spheres are falling through a liquid of density 33

mkg102 with the same uniform speed

the meterical density at sphere 1 and sphere 2 are 33

mkg108 and 3

3

mkg1011 respectively. The

ration of their radii is.

(A) 811

(B)811

(C) 23

(D)23



234

212. Water is flowing continuously dram a temp having an internal diameter m108 3 . The water velocity

as it leaves the tap is 0.4 m/s. The diameter of the water stream at a distance m102 1 below thetap is close to

(A) m100.5 3 (B) m105.7 3 (C) m106.9 3 (D) m106.3 3

213. A large open tank has two holes in the wall one is a square hole of side L ata depth y froam the topand the other is a circular hole of radius R at a depth ay from the top. When the tank is completelyfilled with water the quantities of water following out per second from both the holes are the somethen R is equal to

(A) L2 (B) 2L

(C) L (D)2

L

214. A block of ice floats on a liquid of density 1.2 in a beaker then level of liquid when ice completelymelt.(A) Remains same (B) Rises (C) Lowers (D) (A) (B) or (C)

Assertion & Reason type questionsRead the assertion and reason carefully to mark the correct option out of the options given below(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.(c) If assertion is true but reason is false.(d) IF the assertion and reason are false.(e) If assertion is flase but reason is true.

215. Assertion : The blood pressure in humans is greater at the feet than at the brain.Reason : Pressure of liquid at any point is proportional to height clensity of liquid.(A) a (B) b (C) c (D) d

216. Assertion : To empty an oil tank two holes so it will made.Reason : Oil will come out of two holes so it will be emptied faster.(A) a (B) b (C) c (D) d

217. Assertion : A bubble comes from the bottom of a lake to the top.Reason : Its radius increases.(A) a (B) b (C) c (D) d

Ordinary ThinkingThermometary

218. Oxygen boils at 1830C. This temperature is approximately.(A) 2150 F (B) -2970 F (C) 3290 F (D) 3610 F



235

219. The resistance of a rasistance thermometer has values 2.71 and 3.70 ohm at 100C and 1000C. Thetemprature at which the resistance is 3.26 ohm is(A) 400 C (B) 500 C (C) 600 C (D) 700 C

220. Maximum density of H2O is at the temprature.(A) 320 F (B) 39.20 F (C) 420 F (D) 40 F

221. At what temprature the centigrade (celsius) and Fahrenheit readings at the same.(A) -400 (B) +400 C (C) 36.60 (D) -370 C

222. Mercury thermometers can be used to measure tempratures up to(A) 1000 C (B) 2120 C (C) 3600 C (D) 5000 C

223. If temperature of an object is 1400 F then its temperature in centigratde is(A) 1050 C (B) 320 C (C) 1400 C (D) 600 C

224. When the room temprature becomes equal to the dew point the relative humidity of the room is(A) 100 % (B) 0 % (C) 70 % (D) 85 %

225. If the length of a cylinder on heating increases by 2% the area of its base will increase by.(A) 0.5 % (B) 2 % (C) 1 % (D) 4 %

226. Density of substance at 00C is 10 gm/cc and at 1000Cits density is 9.7 gm/CC. The coefficient oflinear expansion of the substance will be(A) 102 (B) 10-2 (C) 10-3 (D) 10-4

227. A beaker is completely filled with water at 40C It will overflow if(A) Heated above 40C(B) Cooled below 40C(C) Both heated and cooled above and below 40C respectively(D) None of these

228. An iron bar of length 10m is heated from 00C to 1000C. If the coefficient of linear thermal expansion

of iron is C1010 6

the increase in the length of bar is

(A) 0.5 cm (B) 1.0 cm (C) 1.5 cm (D) 2.0 cm

Calorimetry229. Melting point of ice.....

(A) Increases with increasing pressure (B) Decreases with increasing pressure(C) Is independent of pressure (D) is proportional of pressure

230. Amount of heat required to raise the temprature of a body through 1k is called it is(A) Water equivalent (B) Thermal capacity(C) Entropy (D) Specific heat

231. A vessel contains 110 g of water the heat capacity of the vessel is equal to 10 g of water The initicaltemprature of water in vessel is 100C If 220 g of hot water at 700C is poured in the vessel the Finaltemperature meglecting radiation loss will be(A) 700 C (B) 800 C (C) 600 C (D) 500 C



236

232. In a water fall the water falls from a height of 100 cm. If the entire K.E. of water is converted in toheat the rise in temperature of water will be(A) 0.230 C (B) 0.460 C (C) 2.30 C (D) 0.0230 C

233. The temprature at which the vapour pressure of a liquid becomes equals of the external pressure isits.(A) Melting point (B) sublimation point(C) Critical temprature (D) Boiling point

234. 10 g of ice at 00C is mixed with 100 g of water at 500 C what is the resultant temprature of mixture.(A) 31.20 C (B) 32.80 C (C) 36.70 C (D) 38.20 C

Critical Thinking235. Two metal strips that constituate a thermostant must necessarily in their

(A) Mass (B) Length(C) Resistivity (D) Coefficient of liner expansion

236. 2 kg of Ice at -200 C is mixed with 5 kg of water at 200 C in an insulating vessel having a megligibleheat capacity calculate the final mass of water remaining in the container. It is given that the specificheats of water and ice care 1 keal/kg per0C and 0.5 Keal/kg 10C while the latent heat of fusion ofice is 80 kcoil/kg.(A) 7 kg (B) 6 kg (C) 4 kg (D) 2 kg

237. A lead bullet at 270 C just melts when stopped by an obstancle Assuming that 25% of heat isobsorbed by the obstacle then the velocity of the bullet at the time of striking.[M.P. of lead = 3270 C, specific heat of lead = 0.03 cal/x latent heat of fusion of lead = 6 cal/g andJ = 4.2 Jute / cal](A) 410 m/s (B) 1230 m/s (C) 307.5 m/s (D) None of these

238. An electric kettle takes 4A current at 220V How much time will it take to boil 1 kg of water fromtemprature 20C ? The temprature of boiling water is 100 C.(A) 12.6 min (B) 4.2 min(C) 6.3 min (D) 8.4 min

Graphical options239. Ablock of ice at -100C is slowly heated and covered to steam at 1000 C which of the following

curves represents the phenomenon qualitatively.



237

240. The variation of density of water with temprature is represented by the

Assertion & ReasonRead the assertion and reason carefully to mark the correct option out of the option given below.(a) If both asseration and reason are true and the reason is the correct explanation of the reason.(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.(c) If assertion is true but reason is false.(d) If the assertion and reason both are false.(e) If assertion is false but reason is true.

241. Assertion : The melting point of the ice decreases with increases pressureReason : Ice contracts on melting(A) a (B) b (C) c (D) d

242. Assertion : Fahrenheit is the smallest unit measuring temprature.Reason : Fahrenheit was the first temprature scale used for measuring temprature.(A) a (B) b (C) c (D) d

243. Assertion : Melting of solid causes no change in internal energy.Reason :Latent heat is the heat required melt a unit mass of solid.(A) a (B) b (C) c (D) d

244. Assertion : Specific heat capacity is the cause of formation of land and sea breeze.Reason : The specific heat of water is more then land.(A) a (B) b (C) c (D) d

245. Assertion : The moleculs of 00C ice and 00C water will have same potential energy.Reason : Potential energy depends only on temprature of the system.(A) a (B) b (C) c (D) d

246. Assertion : A beaker is completely filled with water at 40C. It will overflow both where heated orcooled.Reason : There is expansion of water below and above 40C.(A) a (B) b (C) c (D) d



238

Answers Key1 D 42 C 83 B 124 A 165 C 206 B2 B 43 A 84 B 125 D 166 D 207 C3 D 44 B 85 D 126 A 167 A 208 D4 B 45 D 86 A 127 A 168 B 209 B5 C 46 A 87 D 128 D 169 B 210 C6 B 47 D 88 B 129 A 170 D 211 D7 D 48 A 89 C 130 A 171 A 212 D8 D 49 A 90 A 131 D 172 B 213 B9 C 50 B 91 D 132 B 173 B 214 B

10 C 51 D 92 B 133 B 174 C 215 A11 A 52 B 93 C 134 C 175 C 216 C12 B 53 D 94 C 135 A 176 B 217 A13 D 54 C 95 B 136 B 177 A 218 B14 B 55 B 96 A 137 C 178 B 219 B15 B 56 A 97 C 138 A 179 C 220 B16 B 57 A 98 D 139 A 180 A 221 A17 B 58 D 99 C 140 A 181 B 222 C18 D 59 A 100 A 141 A 182 E 223 D19 D 60 C 101 A 142 D 183 A 224 A20 D 61 C 102 B 143 D 184 C 225 D21 B 62 B 103 D 144 C 185 B 226 D22 B 63 A 104 D 145 A 186 A 227 C23 C 64 C 105 B 146 D 187 B 228 B24 B 65 C 106 C 147 C 188 C 229 B25 C 66 C 107 B 148 D 189 B 230 B26 D 67 A 108 C 149 D 190 B 231 D27 B 68 B 109 A 150 D 191 C 232 A28 D 69 C 110 D 151 D 192 B 233 D29 A 70 B 111 D 152 C 193 D 234 D30 A 71 A 112 A 153 C 194 C 235 D31 B 72 B 113 D 154 B 195 B 236 B32 D 73 A 114 A 155 A 196 D 237 A33 D 74 B 115 D 156 B 197 D 238 C34 D 75 C 116 A 157 D 198 D 239 A35 D 76 B 117 A 158 C 199 A 240 A36 D 77 A 118 B 159 A 200 D 241 A37 A 78 C 119 C 160 C 201 A 242 C38 C 79 D 120 B 161 B 202 B 243 E39 C 80 B 121 B 162 C 203 A 244 A40 A 81 C 122 B 163 B 204 C 245 D41 D 82 B 123 D 164 C 205 A 246 A



239

Hint

1.

AVLLAV

yAFV

AyFL

2

22

AFVyAF

As cross sectional area of 2nd wire is 3 times therefore 9F force is required for same elongation.

2. Stress Lstressstrain

3. 2dL

ALL

AFY

2dL

(As F and Y are constant)

The ratio of 2dL

is maximum for case CD

4. Young modulus of wire does not vary with dimension of wire. It is the property of given material.5. Depression in beam.

2

3 3wL

4Y bd 1

Y

6. 2

1L r

If radius of the wire is doubled then increament in length will become 1/4 times, i.e. mm34

12

7.YAF

L

8.

A

F

Y Given stress 2

8

mN1018.3

F/A Y

l

9. Here 2k

KQ p

According to Hooke's law ppp xkF

Qp FF (Given) 1....kPkQ

xx

Q

p



240

Energy stored in a spring is

2kpkQ

21

pkQk

kQkp

QxPx

kk

UU

2

2

2

2

q

p

Q

p 2E

2UQUP

10. Breaking force area of crossection of 2r wire

If radius of wire is doubled then breaking force will become four times.

11.2

2LY

12. Young's modulus of material

strainalLongitudinstressLinear

If longitudinal strain is equal to unity, thenY = Linear stress produced

13. Energy stored per unit volume

strainstress21

14. Vstress.MaxstrainMax

StrainstressY

YA

mg

strainMax

15. m106.9

10528.95.1108

Y2dgL 11

8

222

16. stress 2r1stress

Areaforce

AB

22

A

B S4S2Br

rASS

17. Breaking force area of cross section of wire.i.e. load hold by the wire does not depend upon the length of the wire.

18. AYFL

2r1

(F, L & Y are constant)

19. 26 m10A IAY

20. 2r1

AYFL

(F, Land Y are same)



241

21.Steel

1

1

Steel

YYa

aAYFL

(F, Land Y are constant)

22. If length of the wire is doubled then strain = 1AreaForcestressY

23. dgPL

24. F = force developed AYA

25. lateral strainlongitudinal strain

26.strainYFA

strainAF

Yx

27. Strain & stress AF

28. Elongation in the wire AYTL

Elongation in wire tension in the wirein first case 1T wand in second case

www

w2T2

As Tension in the wire in both the cases are equal. Elongation in the wire will be equal.

29.FAYAl

30. 22 r1

yrF


31. Longitudinal strain stress= =L Yl

32. It is the specific property of a particular material at a given temperature which can be changed onlyby temperature variations.

33. When the length of wire is doubled then L and strain = 1

AFstrainY

34.LrF

LAYF

2

(y and L are constant)



242

35. 100 103

7rrY

36. Increase in tension of wire QYA

37.AYFstrain

strainAF

Y

38.L

ALY21W

2

39. Potential energy stored in the rubber cord calapult will be covered into kinetic energy of mass

LYAL

21mv

21 2

2

40. AYFL

A1

(F, L and Y are constant)

mm05.021.0

221

84

AA 1

22

1

1

2

41. ttanconsstrainstressY It depends only on nature of material.

42. AYFL

Final length = initial lengh + increament = 2L

43. AYFL

44. YroK

45. VYFL

YALFL

AYFL 22

2L If the volume of wire remains constant.

46. 22 rF

YrFL

AYFL

(Y = constant)

47. Breaking stress = Strain young's modulus48. In accordance with Hook's law

49. StrainYAF



243

50. Because strain is a dimensionless and unitless quantity.

51. areaforcestress

In the present case,force applied and area of cross-section of wires are same. Therefore stress has to be the same.

Strain = stress /YSince, the young's modulus of steel wire is greater than the copper wire, therefore strain in case ofsteel wire is less than that of in case of copper wire

52. Knowledge base

53. Breaking force 2r

If diameter becomes double then breaking force will become four times

i.e. N400041000

54. AYFL

YALFL

AYFL 22

If volume is fixed then 2L

55. Young's modulus strainstress

As the length of wire get doubled therefore strain = 1

28

mN1020strainY

56. Because dimension of invar does not vary with temperature.

57. yrFL

2

2rL

(Y & F are constant)

58. Q1LandQ1 111222

11221212 Qll

now 0,SoLL 11221212

59. Thermal stress = Qy

60. LYAF

61. 22

1Y

FL rr y

(F, Land l are constant)



244

62. yrFL

2

A1


2 1

1 2

AA

63. Y MgLA

64. AYFL

2rF

65.mgLLYA

66. Work done 2MgF

21

67. Volume

Ystress

21w

2

As F, A and Y are same - W volume (area is same)

w (V = A1)

21

2ww 1

2

1

2

1

68. F21w

69. 2k21k

21F

21wandFK

70. 2

2

rLU;

AY2FF

21U

(F and Y are constant)

71. F21U

72. Volume

Ystress

21U

2

73. When a wire is stretched through a length then work has to be done. This work is stored in the wirein the form of elastic potential energy.Potential energy of stretched wire is

strainstress21U Fx

21U6F

21U



245

74. 2strainYX21U

75. L2YAw

2

76.K2

TK2

FU22

77. Energy stored per unit volume

LAF

21

AL2FL

78.2

LYA

21U

79. At extension l1 the stored energy 21k

21 At extension l2 the stored energy 2

1k21

Work done in increasing its extension from l1 to 21

222 k

21

80. XFK

81. Isothermal elasticity ki = P

82. 1001%1

VVgiven

VBVP

YPVB

28

10

mN105.1

100105.1P

83. Ratio of adiabatic & isothermal elasticities

V

PP

CCV

PV

84. For triatomic gas 34V

85.

vv

Pk

86. PvvC

CC4.0



246

87.

vv

hsg

vvPk

88. If side of cube is L then LdL3

vdvLV 3

89.2

122

116

cmdynes10

mN10atm10

10001.0

100k

90. If the coefficient of volume expansion is and raise in temprature is then

vv

vv

volume elasticity

P

vv

P

91. If side of the cube is L then V = L2

LdL3

vdv

% change in voulume 3 (% change in length) %3%13

Bulk modulus 03.0vv

92. Adiabatic elasticity vp

For Argon EAr = 1.6 pFor hydrogon EH2 = 1.4 plAs elasticity of hydrogen & Argon are equal

Pl4.1P6.1

P78'P

93. Isothermal elasticity 25

mN10013.1013.1atm1KiP

94. Isothermal bulk modulus = pressure of gas

95. dv dL1 2v L

215.061041022

vdv 33

96. We know that L

dL21v

dv If 0

vdvthen

21

i.e. there is no change in volume



247

97. Y = 2N ( 1 + )

98. n

ny5.01n2Y

99. Twisting coulple

2rnC

4

If material and length of the wires A and B equal twisting coulple are applied then

4r1

4

1

2

2

1

rr

100. Value of possion's ratio die in range of 1 to 1/2.

101. 1n2y;21k3y

For Y=0 we get 021 also 01

lies between

102. 1n2n31n2y211

23

Now, substituting the value of in the following expression

213yk

103. 1n2Y104. There will be both shear stress and normal stress.

105. Angle of shear '12.0'30100

104Lr 1

106. For twisting, angle of shear L1

i.e. if L is more then will be small

107. 004.028.010Lr 2

108. 1n2Yand21K3Y Eliminating we got k3nnk9Y

109. Poisson's ratio varies between - 1 and 0.5

110. MTkn2T 2

If we draw a graph of between T2 & M then it will be straight line and for 0T;0M 2

i.e. graph should pass through the origin but from the graph it is not reflected it means the mass ofpan was neglected.



248

111. In the region OA, stress strain . i.e.Hooke's las hold good.112. As stress is shown on X axis and strain on Y axis so we can say that

slope1

tan1cotY

So elasticity of wire P is minimum and of wire R is maximum.113. Area of hysterisis loop gives the energy loss in the process of stretching and understretching of

rubber band and this loss will appear in the form of heating.

114.tantan

YY

B

A

B

A

115. i.e.for the same load thickest wire will show minimum elongation so graph D present the thickestwire.

116. From the graph N20F,M10 4 M1,M10A 26

46 1010120

AlFLY

21110

mN1021020

117. At point b yeilding of material starts.118. Graph between applied force and extension will be straight line because in elastic range.

Applied force extension. but the graph between extension and stored elastic energy will be parabolicin nature.

As 22 xUorkx21U

119.

dxdvF

In the region BC slope of the graph is positive. F negative i.e. force is attractive in nature.

In the region AB slope of the graph is negative. F positive i.e. force is repulsive in nature.

120. Force constant K = tan 300 3

1

121. In ductile materials, yeild point exist which in brittle material failure would occur without yeilding.

122. Young's modulus is defined strainstressY

123. Elasticity of wire decreases at high temperatare i.e. at higher temprature slope of graph will be less,So T1 > T2.

124. Attraction will be minimum when the distance b/w the molecule is maximum. Altraction will bemaximum at that point where the positive slope is maximum b'sc

duFdx



249

125. B'se stretching of coil simply chnages its shape without any change in the length of the wire used incoil Due to which shear of elasticity is prevolved.

126. A bridge during its use undergoes alternating strains for a large number of times each day dependingupon the movement of vehicle on it. When a bridge is used for long time. It losses its strength Due towhich the amount of strain in the bridge for a given stress will become large and ultimately the bridgemay collapse. This may not happen if the fridges are declared unsafe.

127. Ivory is more elastic than wet-clay. Hence, the ball of ivory will rise to a greater height. Infact the ballof wet day will not rise at all it will be same, what flattended permanently.

128. Young's modulus of a material.strainstressY

Here, stress force forceAreastaringRe

As restoring force is zero. 0Y

129. Work done 2strainY21strainstress

21

Since, elasticity of steel is more than copper,,

hence, more work has to be done in order to stretch the steel.

130.

yxAFt

133.

A

AW

Y

139. LL

AFY



250

Hint143. Soap helps to lower the surface tension of solution thus soap get stick to the dist partcles and grease

and these are removed by action of water.

145. Force required to separate the plates t

TA2F

147.

r2cosTcoaterdisplacedofweight

cosrT2w

148. mgTL2 L2

mgT

149. 21

22 RRT8w 22 rr2T8 Tr24 2

150. 21

22 rr8Tw

4d

4D8T

22

TdD2 22

151. Energy spent = T increase in surface ared

22 r4r242T JoulerT24 2

152. ATw

153. Surface energy = Surface tension surface ared

A2TE

New surface energy

2A2TF1

% decrase in surface energy 100E

EE i

154. The ration of the total surface energies before and after the change 1:n 21

1:231

155. TR8w 2

156. ATw A

wT

157. 3R34



251

158. As volume remains constant 33 r8000R r20R

1r48000TR4

dropsmall8000ofenergySurfacedropbigoneofenergySurface

2

2

159. Tension Areaenergysurface

AETor

160. Angle of contact is a 00

165. RT2p

167. BABA PPSor1pandrr

So air will flow from B to A i.e. size of A will increase

168. hdgRT4

4RhdgT

mN109.3 2

169. Mass of liquid in capillary tube

2RM

R1RM 2

RM If radius become double then mass will become twice.

172.rdg

T2h r1h 2211 hrhr

173. cm0.460coscos

h

174. When a capillary tube is broken at a height of 6 cm the height of water column will be 6 cm.

As ttanconscos

horrg

cos25h

43

80cos6cosor

cos6

0cos8 o

o

43cos 1

175. Rise in tempreture

R1

r1

JsdT3

R1

r1

JT3

(For water S = 1 and d = 1)

176. rdgcosT2h

r1h so the graph between h and r will be rectangular hyperbold

rT4p

r1p As radius of soap bubble increases with time t

1P



252

178. tIToTC

i.e. Surface tension decreases with increase in temperature179. Due to surface tension vertical force on drop

SmrTFv 2

Rr2T

RrrT

2

2

180. 9.R34T

Rr2 3

2

181. 23104.1411.0ATU

183. dgT2hR

RdgT2h constanthR

Hence when the tube is of insufficient length radius of curvature of the liquid meniscus increasses soas to maintain the product hR a finite constant.i.e. as h decreases R increases and the liquid meniscus becomes more and more flat but the liquiddoes not overflow.

184. The presence of impurities either on the liquid surface or dissolved in it considerably affect the forceof surface tension depending upon the degree of surface tension depending upon the degree ofcontamination. A highly soluable substance like sodium chioride when dissolved in water increasethe surface tension. But the sparing soluable or substance like phenol when dissolved in waterreduces the surface tension of water.

185. We know that the intermolecular distance between the gas moleculas is Large as compaired to thatof liquid Due to it the forces of cohesion in the gas moleculas are very small and these are quiteLarge for liquids. Therefor the concept of surface tension is applicable to Liquid but not to gasses.

186. The height of capillary rise is inversly propostional to radius (or diametre) of capillary tube

i.e. r1h so, for smaller r the value of his higher

187. When a drop of Liquid is poured on a glass, plate, the shape of the drop also is governed the forceof gravity for every small drops the potential energy due to gravity is insignification. Compared tothat due to surface tention. Hence, in this case the shape of the drop is determined by sufrace tensionalone and drope becomes spherical.

188. 2211 vpvp

303 r2

34pr

34ghp



253

189. Thrust on lamina = pressure at centroid area

1 A3 3

h g A gh

190. Bulk modulas

Bpvv

vpVB 00

Bp1vv 0

1

0 Bp1Density

Bp10

191. = 760 - 750 = mnat Hg = 4g192. Here, h = 20 m

Density of water 33

mkg10

Atmospheric pressure

pa1001.1Pa 5

ghpap

193. Weight of the ball = Buyoant force + viscous force194. For the floatation Vo dog = Vin dg

ddoVVin 0

ddoVVVinVVout 000

195. Weight of bodyWeight of water displaced Weight of oil displaced

34oilofgrvitySpecitic

w

0

196. Aschemedies principal explains buoyant force and bouant force depends on acceleration due togravity

204. If two drops of same radius r coalesce then radius of new drop is given by R

33333 r2Rr34r

34R

34

r2R 31

Is drop of radius r is falling in viscous medium then it acquire a critical velocity V and 2rV

2

31

2

1

2

rr2

rR

vv

132

2 v2v 52 32

sm45 3

1



254

206. According to Bernouli's theoram

cm30.0102

45.2h9vh

22

cm0.30

207. Time taken by outer to reach the bottom =

2 H Dt

g

and velocity of water coming out of hole

gD2v

Horizontal distance coveredtvx

209. Terminal speed ngr

92v

2

Where, Density of the substance Density of the liquid

If n and r are constant then

v210. Mass = volume Density

3r34M

As the density remains constant3rM

211. The terminal velocity of the spherical body of radius R density S falling through a liquid of density is given by

229t

RV g

n

where n is the coefficient of vescosity of the liquid.

1

21 1

T

29

RV g

n

2

22 2

t

2and

9R

V gn

According to the given problem



255

212. Diameter m108 3

sm4.0V1

v2 gh2v 21

A1v1 = A2v2

215. The volume of liquid displaced by floating ice

MVD

Volume of water formed by melting ice, wMVF

FD VVe.iw

ML

M

- Height of the blood column in the human body is more at feet than at the brain as P = hpg there face

the blood exeists more pressure at the feet than at the brain.- When to holes are made in the Hn air keeps on externing through the other hole Due to this the

pressure inside the tin does not become less than at mosphere pleassure which happen only whenhole is made.

218. F297F932F

5183

932F

5C o

219. Change in resistonce 99.071.270.3 to interval of temprature 900 C so change in resistance 55.071.226.3 corresponds to change in temprature.

C5055.099.0

90 o

220. Maxmimum density of water is at 40 C also

932F

5C

221. 932F

5C

222. The boiling point of mercury is 4000 C. Therefore the mercury thermeter can be used to measure therange upto 3600 C.

223. 932F

5C

225. LL.2

AALA 2



256

226. Coffcient of volume expansion

21

T.r

Hence, cofficent of linear expansion227. Water has maximum density at 40C so if the water is heated above 40C or Density cooled below

40C density decreases. In other words it expands so it overflows in both cases.

228. Increase in length LoL

Calorimetry229. Melting point of ice decreases with increase in pressuire.

230. capacityThermalmcthenk1if;c.m

231. Let final temprature of water bc heat taken = Heat given

7012201010101110

C50C8.48 oo

232. 1000023.0h0023.0 C23.0 o

233. At boiling point vapour pressure becomes equal to the external pressure.

234.mwmi

cwmiLiwmw

mix

Critical Thinking235. Thermostat is used in electric opporatas like refrigerator iron etc for automatic cut off Therefore for

metallic strips to bend on heating their coefficient of linear expansion should be different.236. Initially ice will absorb heat to rise its temprature to 00C then its melting takes place. If mi = Initial

mass of ice mi-1 = Mass of ice that melts and mw = Initial mass of water By low of mixture Heatgained by ice = Heat lost by water 20mwCLmi20cmi w

kg1mi201580mi205.02 7

So final mass water Initial mass of water + mass of ice that melts = 5 + 1 = 6 kg237. If mass of the bullet is m gm then total heat required for bullet to just melt down.

mLmc1

Now when bullet is stopped by the obstacle the loss in its mechanical energy 9v)10cm21 23

(As kg10mmg 3 )As 25% of this energy is absorbed by the



257

2 10mv8310mv

21

10075 3232 J

Now the bullet melt if 12

238. mctP

VIm4200

pm4200

pmct

Ckg14200water o

min3.6sec3814220

2010014200t

Graphical Optaions239. Initially on heating temprature rises from -100 C to 00 C Then ice melt and temprature does not rise

After the whole ice has melted temprature begins to rise until reaches 1000 C Then it becomesconstant as at the boiling point will not rise.

240. Density of water is maximum at 40 C and is less on either side of this temprature.

Assertion & Reason241. With rise in pressure melting point of ice decreases also ice contracts on melting.242. Celsius scale was the first temprature scale and fahrenheit is the smallest unit measuring temprature.243. Melting is associated with increasing of internal energy without change in temprature in view of the

reason being correct the amount of heat absorbed or given out during change of state is expressedwhere m is the mass of the substances and L is the latent heat of the substance.

244. If bath assertion and reason are true and the reason is the correct explanation of the assertion.245. The potential energy of water molecules is more. The heat given to melt the ice at 00C used up in

increasing the potentical energy of water molecules formed at 00 C246. Water has maximum density at 40 C on heating above 40 C or cooling below 40C density of water

decreases and its volume increases. Therefore water overflows in both the cases.



NEET UG Physics Properties of Liquid of Solid MCQs

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