Topper’s Package Physics - XI Permutation and Combinations

Topper’s Package Physics - XI Permutation and CombinationsProperties of Matter

95

1. STRESS, STRAIN AND MODULUS OF ELASTICITY1. If the small solid identical balls of ivory and

clay are dropped form the same height, thenthe ivory balls rises higher after reboundingfrom floor because(a) ivory ball is more expensive(b) ivory ball is smaller in size(c) ivory ball is more elastic than clay(d) ivory is less elastic than clay

2. A force of 400 kg weight can break a wire. Theforce required to break a wire of double thecross-section will be(a) 800 kg-wt. (b) 200 kg-wt.(c) 1600 kg-wt. (d) 100 kg-wt.

3. A steel wire of length 4 meter and diameter5mm is stretched by 5 kg-wt. The increase inits length will be, (the Young’s modulus of steelwire is Y 12 22.4 10 /dynes cm )(a) 0.416 cm (b) 0.00416 cm(c) 0.0416 cm (d) 0.416 meter

4. The lengths and radii of two wires of samematerial are respectively L, 2L and 2R, R. Equalweights are applied on them. If the elongationsproduced in them are 1l and 2l respectivelythen their ratio will be(a) 2 : 1 (b) 4 : 1 (c) 8 : 1 (d) 1 : 8

5. From the graph between the restoring force (D)and displacement (x), the value of forceconstant will be(a) 3/2

(b) 3

F

30° x

(c) 1/ 3

(d) 1/2

6. The ratio of radii of two wires of same materialis 2 : 1. If these wires are stretched by equalforce, then the ratio of stresses produced inthem will be(a) 1 : 2 (b) 2 : 1 (c) 1 : 4 (d) 4 : 1

7. A steel wire of uniform cross-section of 22 mmis heated upto 50°C and clamped rigidly at twoends. If the temperature of wires falls to 30°Cthen change in tension in the wire will be,(coefficient of linear expansion of steel is

51.1 10 / C and Young’s modulus of elasticityof steel is 11 22 10 /N m )(a) 44 newton (b) 88 newton(c) 132 newton (d) 22 newton

8. If the increase in length of a wire is equal toits initial length, the Young’s modulus ofelasticity of its material is equal to(a) Stress/Strain (b) Strain(c) 2 × Stress (d) Stress

9. The correct graph verifying Hook’s law is

(a)

Load

Exte

nsio

n

(b)

Load

Exte

nsio

n (c)

Load

Exte

nsio

n

(d)

Load

Exte

nsio

n

10. The modulus of elasticity of a material doesnot depend upon(a) Shape (b) Temperature(c) Nature of material (d) Impurities mixed

11. Two identical wires of copper and steel arejoined and a force is applied on them so thatthe combined length increases by 1 cm. In boththe wires there will be(a) equal stress and equal strain(b) unequal stress and unequal strain(c) equal stress and unequal strain(d) equal strain and unequal stress

12. A steel ring of radius r and cross-section A isto be mounted on a wooden wheel. If theYoung’s modulus of steel is Y, then theminimum tensile force required to be developed

PROPERTIES OF MATTER Unit 8


96

in the ring so that it can easily get mounted onthe wheel, will be (R is radius of wheel)(a) YAR/r (b) YAr/R(c) Y(R – r)/Ar (d) YA(R – r)/r

13. One of the ends of a metal rod of length L issuspended from a ceiling. The extensionproduced in the rod under its own weight willbe (Y = Young’s modulus of the material of rodand density of rod)

(a)Y

gL2 (b)Y2

gL2 (c)Y3

gL2(d)

Y4gL2

14. One end of a uniform wire of length L and ofweight W is attached rigidly to a point in theroof and a weight 1W is suspended from its lowerend. If S is the area of cross-section of the wire,

the stress in the wire at a height 4L3

from itslower end is –

(a)S

W1 (b)S

4WW1

(c)S

4W3W1

(d)S

WW1

15. A ball falling in a lake depth 200 m shows 0.1%decrease in its volume at the bottom. What isthe bulk modulus of the material of the ball(a) 8 219.6 10 /N m(b) 10 219.6 10 /N m(c) 10 219.6 10 /N m(d) 8 219.6 10 /N m

16. The potential energy U between the twomolecules as a function of the distance xbetween them is shown in fig. A. B and C arepoints for which x = 0.6 Å , 1.2 Å and 1.8Å. At A.B and C force between the two moleculesrespectively is

0.6 Å 1.2 Å 1.8 Å

U

0,0 A B C x

(a) attractive, zero, repulsive(b) zero, attractive, repulsive(c) repulsive, zero, attractive(d) zero, repulsive, attractive

17. The dimensions of two wires A and B are thesame. But their materials are different. Theirload-extension graphs are shown. If AY and BYare the values of Young’s modulus of elasticityof A and B respectively then

(a) A BY Y ]

(b) A BY Y

A

B

Load

Extension

(c) A BY Y

(d) 2B AY Y

18. Figure shows the stress-strain lines for brass,steel and rubber. The lines A, B and C are for

B

Stre

ss

Strain

A

C

(a) steel, brass and rubber respectively(b) brass, steel and rubber respectively(c) steel, rubber and brass respectively(d) rubber, steel and brass respectively

19. A wire elongates by l mm when a load W ishanged from it. If the wire goes over a pulleyand two weight W each are hung at the twoends, the elongation of thewire will be (in mm)

(a)2l

(b) l (c) 2l (d) zero

20. A man grows into a giant such that his lineardimensions increase by a factor of 9. Assumingthat his density remains same, the stress inthe leg will change by a factor of

(a) 9 (b)19 (c) 81 (d)

181

21. A uniformly tapering conical wire is made froma material of Young’s moduls Y and has anormal, unextended length L. The radii, at theupper and lower ends of this conical wire, havevalues R and 3R, respectively. The upper endof the wire if fixed to a rigid support and a massM is suspended from its lower end. Theequilibrium extended length, of this wire, wouldequal

(a)

2

2L 19

MgYR

(b)

2

1L 19

MgYR


97

(c)

2

1L 13

MgYR

(d)

2

2L 13

MgYR

2. ENERGY DENSITY IN ELASTIC MATERIAL

22. The workdone in twisting a steel wire of length0.25 meter and radius 1 mm through an angleof 45° will be if 108 10 pascal(a) 15 Joule (b) 0.15 Joule(c) 1.5 Joule (d) 0.015 Joule

23. The potential energy of a metallic rod when itis compressed(a) increased (b) remains constant(c) decreased (d) becomes infinite

24. Calculate the work done, if a wire is leaded by‘Mg’ weight and the increase in length ‘l’(a) Mgl (b) zero (c) Mgl/2 (d) 2Mgl

25. An ealstic material of Young;s modulus Y issubjected to a stress S. The elastic energystored per unit volume of the material is

(a) 22YS (b)

2

2SY

(c) 2SY (d)

2SY

26. Wires A and B are made from the samematerial. A has twice the diameter and threetimes the length of B. If the elastic limit arenot reached, when each is stretched by thesame tension, the ratio of the energy storedin A to that in B is(a) 2 : 3 (b) 3 : 4(c) 3 : 2 (d) 6 : 1

27. A wire of length L and cross-sectional area Ais made of a material of Young’s modulus Y. Itis streched stretched by an amount x. Thework done (or energy stored is)

(a) 2YxA

L (b)2Yx AL

(c)2

2Yx A

L(d)

22Yx AL

28. A stretched wire(a) Increased kinetic energy(b) Increased potential energy(c) Decreases kinetic energy(d) Decreased potential energy

29. If a spring extended by x on loading, then theenergy stored by the spring is (if T is tensionin the spring and k is spring constant)

(a)2

2T

x(b)

2

2T

k

(c) 22xT (d)

22Tk

30. Young’s modulus of the material of a wireY. On pulling the wire by a force F, theincrease in its length is x. The potentialenergy of the stretched wire is

(a) 12

Fx (b) 12

Yx

(c) 212

Fx (d) None of these

31. K is the force constant of a spring. The workdone in increasing its extension from l1 tol2 will be

(a) K(l2 – l1) (b) 2 1( )2K l l

(c) 2 22 1( )K l l (d) 2 2

2 1( )2K l l

32. If x longitudinal strain is produced in a wireof Young’s modulus Y, then energy stored inthe material of the wire per unit volume is(a) Yx2 (b) 2 Yx2

(c) 212

Y x (d) 212

Yx

33. A metal rod of length ‘L’ cross sectional area‘A’. Young’s modulus ‘Y’ and coefficient oflinear expansion ‘a’ is heated to ‘t°C. Thework that can be performed by the rod whenheated is(a)

2

2YA L t (b)

2 2

2YA L t

(c)2 2 2

2YA L t (d) 2

YA L t

34. Two springs P and Q of force constant kp and

2p

Q Q

kk k

are stretched by applying forces

of equal magnitude. If the energy stored inQ is E, then the energy stored in P is(a) E (b) 2E(c) E/8 (d) E/2

35. The length of a wire is 1.0 m and the areaof cross-section is 1.0 10–2 cm2. If the workdone for increase in length by 0.2 cm is 0.4joule, the Young’s modulus of the materialof the wire is(a) 2.0 1010 N/m2 (b) 4.0 1010 N/m2

(c) 2.0 1011 N/m2 (d) 4.0 1011 N/m2


98

36. A rubber cord catapult has has cross-sectionalarea 25 mm2 and initial length of rubber cordis 10 cm. It is stretched to 5 cm and thenreleased to project a missile of mass 5 gm.Taking Yrubber = 5 108 N/m2 velocity of theprojected missile is(a) 20 ms–1 (b) 100 ms–1

(c) 250 ms–1 (d) 200 ms–1

37. The graph shows the behaviour of a lengthof wire in the region for which the substanceof obye’s Hooke’s law. P and 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

3. FLUID STATISTICS

38. The height of water level in a tank is H. Therange of water stream coming out of a hole at

depth 4H

from upper water level will be

(a)2

H3(b) 3

H2

(c) 3H

(d) H3

39. What would be the volume of a balloon filledhydrogen gas, which can lift a 25 kg weight inair, if the densities of air and hydrogen are

5 3129 10 /gm cm and 5 39 10 /gm cm re-spectively(a) 320.8 m (b) 310.4 m(c) 32.08 m (d) 30.20 m

40 The difference of two liquid levels in amanometer is 10 cm and its density is

30.8 /gm cm . If the density of air is3 31.3 10 /gm cm then the velocity of air will

be (in cm/sec)(a) 347 (b) 34.7(c) 3470 (d) 0.347

41. A water tank is filled with water upto a heightH. A hole is made in the tank wall at a depth Dfrom the lower end of wall then the distance

where the water stream from tank strikes theground is

(a) gD2 (b) DHD2 (c) DHD2 (d) D

42. A small sphere of mass M and density 1D isdropped in a vessel filled with glycerine. Ifthe density of glycerine is 2D then the viscousforce acting on the ball will be in Newton.

(a) 1 2M D D (b) Mg

1

2DD1

(c)2

1

MD gD (d) 21 DD

gM

43. There is small hole of diameter 2 mm in thewall of water tank at a depth of 10 m below freewater surface. The velocity of efflux of waterfrom the hole will be(a) 0.14 m/s (b) 1.4 m/s(c) 0.014 m/s (d) 14 m/s

44. A sample of metal weights 210 grams in air,180 grams in water and 120 grams in anunknown liquid. Then(a) the density of metal is 33 /g cm(b) the density of metal is 37 /g cm(c) density of metal is 4 times the density of

the unknown liquid(d) the metal will float in water

45. A wooden cube first floats inside water when a200 g mass is placed on it. When the mass isremoved the cube is 2 cm above water level.The side of cube is(a) 5 cm (b) 10 cm(c) 15 cm (d) 20 cm

46. A solid uniform ball having volume V anddensity floats at the interface of twounmixble liquids. The densities of the upperand the lower liquids are 1 and 2respectively, such that 1 2 . Whatfraction of the volume of the ball will be in thelower liquid ?

(a)21

2ρρρρ

(b)21

1ρρ

ρ

(c)21

1ρρρρ

(d)2

21ρρρ

47. Water contained in a tank flows through anorifice of diameter 2 cm, under a constantpressure difference of 10 cm of water column.The rate of flow of water through the orifice is


99

(a) 44 c.c./sec (b) 4.4 c.c./sec(c) 440 c.c./sec (d) 4400 c.c./sec

48. The reading of a spring balance when a blockis suspended from it in air is 60 N. This readingis changed to 40 N when the block is submergedin water. The specific gravity of the block mustbe therefore(a) 3 (b) 2 (c) 6 (d) 3/2

49. A large open tank has two holes in wall. One isa square hole of side L at a depth y from the topand the other is a circular hole of radius R at adepth 4y from the top. When the tank iscompletely filled with water, the quantities ofwater flowing out per second from both the holesare the same. Then, R is equal to

(a) 2L

(b) 2 L (c) L (d)2L

50. A homogeneous solid cylinder of length L (L <H/2), cross-sectional area A/5 is immersedsuch that it floods with its axis vertical at theliquid-liquid interface with length L/4 in thedenser liquid as shown in the figure. The lowerdensity liquid is open to atmosphere havingpressure P0. Then, the density of the solid isgiven by

(a)54

d

(b)45

dH

2d

d

(c) 4d

(d)5d

51. Water is filled in a cylindrical container to aheight of 3m. The ratio of the cross-sectionalarea of the orifice and the beaker is 0.1. Thesquare of the speed of the liquid, coming outfrom the orifice at a height of 52.5 cm fromthe bottom, is ( 210 /g m s )(a) 2 250 /m s (b) 2 250.5 /m s(c) 2 251 /m s (d) 2 252 /m s

52. A wooden block, with a coin placed on its top,floats in water as shown in the figure in thefigure. The distances l and h are as shown inthe figure. After sometime the coil falls intothe water. Then

l

h

(a) l decreases and h increase(b) l increases and h decreases(c) both l and h increases(d) both l and h decreases

53. When at rest, a liquid stands at the same levelin the tube. But, as indicated in diagram, aheight difference h occurs when the system isgiven an acceleration a towards the right. Hereh is equal to

(a)2aL

g

(b)2gLa

h

a

L(c)gLa

(d)aLg

54. A U-shaped tube contains a liquid of density and it is rotated about the line as shown inthe figure. The difference in thelevels of theliquid column is

(a)2 2

2Lg

(b)2 2Lg

(c) 2Lg

(d)L

g

55. A liquid X of density 33.36 /g cm is poured ina U-tube, which cointains Hg. Another liquid Yis poured in left arm with height 8 cm , upperlevels of X and Y are the same. What is thedensity of Y

(a) 1.2 / . .gm c c

(b) 0.8 / . .g c c

8cm 10cm

XY

(c) 1.4 / . .gm c c

(d) 1.6 / . .g c c

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Topper’s Package Physics - XI Permutation and Combinations