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MECHANICS

SECTION 1

QUESTIONS 1. Two vectors have magnitudes in the ratio 1:2. Their vector sum is perpendicular to the smaller vector.

The angle between the vectors is a) 1500 b) between 1500 and 1200

c) 1200 c) between 1200 and 900

2. Two satellites A and B revolve round earth in circular orbits of radius r and 1.01r. The percentage increase in the period of B with respect to A is

a) 0.5 b) 0.75 c) 1 d) 1.5 3. Which of the following pair has not same dimension? a) Curie and angular velocity b) velocity gradient and frequency of light c) Gravitational field and latent heat d) potential gradient and force per unit charge 4. Three particles of same mass rest on the corners of an equilateral triangle. The gravitational force

between any two of them has a magnitude F. Then gravitational force on any of them has magnitude a) F b) 2F c) √3 F d) √2 F 5. The momentum of a car is increased by 10% and then decreased by 10%. In the process the kinetic

energy of car a) increases by 2% b) decreases by 2% c) increases by 1% d) decreases by 1%

6. The position vector of a particle is j)t(sinai)tcosa(r ω+ω= . The velocity vector is a) perpendicular to position vector b) parallel to position vector c)always directed towards origin d) always directed away from the origin 7. Read the following statements A and B: A: If a quantity has units, it will have dimensions. B: If a quantity has dimensions, it will have units Of these statements a) Both A and B are true b) Both A and B are false c) A is true but B is false d) B is true but A is false

8. The equation of the motion of a body initially at rest is given by dtdv = 8-4v, where v is velocity of the

body at the time. Check the wrong statement a) terminal velocity of the body is 2m/s b) initial acceleration of the body is 8 m/s2

c) the velocity of the body when acceleration is half the initial value is 1 m/s d) velocity is related to time by the equation v = at + bt2 where a and b are constants. 9. A set of N cubical blocks rest on a smooth horizontal table such that distance between 2 near surfaces

of the block is L. The block at one end is given a speed v to the next at the time t = 0. All collisions are perfectly inelastic. then the last block starts to move after a time

v

L)1N(N)d

v2L)1N(N

)cv2

L)1N()b

vL)1N(

)a−−−−

10. In the previous question, centre of mass of the system will have a final speed

a) zero b) 2v c) v d)

Nv

11. A rocket moves with a speed v where air resistance is proportional to the cube of its speed. If the speed of the rocket is to be increased by 1%, the increase in the power will be

a) 1% b) 2% c) 3% d) 4%

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12. Water issuing out as a horizontal jet with a speed v1 at a rate V m3 per second strikes a plate normally moving towards it with a speed v2. If density of water is p and water splashes down after hitting the plate, the force on the plate in newton is

a) pv1 V b) p(v1 +v2) V c) p(v2-v1)V d) 21

21

vvVpv

+

13. Read the following statements carefully. Statements x: A vector quantity has magnitude and direction. Statement y: All quantities, which have magnitude and direction, are vectors. Here a) both statements are correct b) both statements are not correct c) x is correct and y is not d) y is correct and x is not 14. If R is the radius of earth’s orbit round sun, the angular momentum of earth round sun is proportional

to a) R2 b) R3/2 c) R d) R1/2

15. Two particles P and Q move towards each other due to mutual gravitational force. At a certain time the speed of P is v and speed of Q is 2v. The speed of centre of mass of the system is

a) 0 b) v/2 c) 3v/2 d) v 16. Two masses 0.4 and 0.6 kg are suspended from the zeroeth and hundredth cm division of a meter scale

of negligible mass. It is required to rotate the meter scale with constant angular velocity with minimum work. The axis of rotation should pass through at

a) 40 cm b) 50 cm c) 60 cm d) 70 cm 17. An infinite number of point masses m kg each are placed at a distances x = 1cm, x = 2cm, x = 8

cm.....etc from a point 0 on the x-axis. The gravitational potential at the point 0 in J/kg is a) infinity b) zero c) -100 Gm d) -200 Gm 18. A simple pendulum of length L has a bob of mass m. It sis displaced by an angle θ to the vertical. If T

is a tension of a string, v is the speed of the bob then, check the correct statement

a) T = mg cos θ b) T = mg cos θ -L

mv2

c) T = mg cosθ + L

mv2 d) T cos θ = mg

19. The gravitational force between a planet and a satellite varies by a distance law f αrn. The period of the satellite will be independent of distance if n is equal to

a) 1 b) 2 c) -1 d) 3/2 20. Two boys A and B hold two ends of a light rope carrying a 1 kg weight at the centre. If the length of

the rope is 1 metre the work done by the boys to straighten the rope is a) 0 b) infinity c) 4.9 J d) 9.8 J 21. Two particles of mass m each move in a circle of radius r due to their mutual gravitational force. The

period of their motion is

3

333

rGm2 )d

Gmr )c

Gmr4 )b

Gmr2 )a ππππ

22. A car, a truck and a lorry of masses in the ratio 1:2:3 have equal kinetic energy. Their braking forces are also same. When brakes are applied at the same time, they are brought to rest in distances s1, s2 and s3 respectively. Then

a) s1 > s2 > s3 b) s1 < s2 < s3 c) s1 = s2 = s3 d) s1 + s2 = s3

23. A shell is fired with an initial velocity u at an angle α to the horizontal. At highest point on its path, it explodes into two equal fragments. One falls vertically down. The distance between the fragments when they reach the ground is

a) u2 sin 2α/g b) u2 sin 2α/ 2g c) 2u2 sin 2α/ g d) 3u2 sin 2α/ g 24. The time of a flight of a projectile is 4 s. One second after projection it moves at an angle 450. Its

angle of projection is a) 600 b) tan-1 (4/3) c) tan-1 (3/2) d) tan-1 (2) 25. The velocity vector of the projectile in the above question is parallel to i2i3)di3i2)cii2)bi2i)a ++++

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3 26. A fly wheel starting from rest and rotating with uniform angular acceleration turns through 100 rad

during third second. During fifth second it will turn through an angle (in rad) a) 100 b) 166.7 c) 180 d) 200

27. When three forces )kji(xfandkj2i3f,k5j4i3f 321 −+=−+=−+= act on a body, the body moves with uniform velocity. The value of x here is

a) -6 b) 6 c) -9 d) 9 28. A satellite is moving in a circular orbit of radius x around the earth of radius R. The acceleration of the

satellite is

a) g b) xRg)c

xgR

d) g2

2

xR

29. Check the correct statement for a body in uniform circular motion a) the body has constant centripetal force b) the body has varying centripetal force c) the body has constant velocity d ) the body obeys T2 α R3 law

30. A body of mass 2 kg moves with a velocity (3 t. The magnitude of force acting on it at this instant is

)j4i +

a) 6N b) 8N c) 10N d) 7N 31. A particle moves in a parabolic path whose equation is y = 4ax2, with a constant x component of

velocity equal to A. The acceleration of the particle is kaA8)dkaA4)cjaA8)bkaA4)a 222

32. For an earth satellite longer orbits will correspond to a) longer periods and larger velocity b) longer periods and smaller velocity c) smaller periods and smaller velocity d) smaller periods and larger velocity 33. The velocity-time graph of an aero plane moving along a run way is a parabola. This means aero plane

has a) constant but large acceleration b) acceleration proportional to time c) acceleration proportional to square of time d) acceleration proportional to cube of time 34. The period of a simple pendulum with an iron bob is T. It will be less than T, when the bob is

subjected to a) a magnetic field directed upwards b) an electric field directed upwards c) a magnetic field directed downwards d) an electric field directed downwards 35. A body falls from a height h and rebounds from a surface of coefficient of restitution e = 1/√2. The

number of collisions it will make before it stops is equal to a) 1 b) 2 c) 4 d) infinite 36. The total distance travelled by the body before it stops to rebound is a) 2h b) 3h c) 4h d) 3√2h 37. A stone is thrown vertically up. It reaches a maximum height of 50 m. The height at which kinetic

energy becomes 60% of the initial value is (in m) a) 30 b) 50 4.050)c6.0 d) 20 38. A trolley of mass 100 kg moves on a smooth horizontal rails with a monkey of mass 20 kg inside it,

with a speed of 10 m/s. The monkey at some point jumps vertically up and catches overhanging branch of a tree. The speed of the trolley after this would be

a) 12 m/s b) 10 m/s c) 15 m/s d) 8.33 m/s

39. F is a force represented by the vector j4i2F += and s is displacement vector given by .jis += The component of force in the direction of displacement is

a) 23)c2)b20 d) 6

40. A body of mass 1 kg is dropped from the top of a tower on a windy day. The wind exerts a constant horizontal force of 20N on the body. The path of the body will be

a) a parabola b) a straight line c) an ellipse d) an irregular curve

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41. A stone A is dropped from the top of a tower of height 40 m. At the same time another stone B is projected from the bottom of the tower with an initial velocity such that the stones collide midway. The initial speed of second stone B is (Take g = 10 m/s2)

a) 5 m/s b) 10 m/s c) 20 m/s d) 15 m/s 42. A TV signal sent from a station A to Insat 1-C is received back in a neighboring station B in a time t

seconds. The value of t here is nearest to a) 1 s b) 0.1 s c) 0.125 s d) 0.24 s 43. A person is standing at a distance of 8m from a train. The train starts with acceleration 1 m/s2. The

person also starts at the same time with an acceleration 2m/s2. The time in which he catches the train is a) 2 s b) 4s c) 8s d) 16s 44. A particle moves with a constant velocity parallel to the x-axis . Its angular momentum with respect to

the origin a) increases b) decreases c) first increases and then decreases d) remains the same 45. The escape velocity of a body projected at an angle 50 with the horizontal from the earth in (in km/s) is a) 11.2 b) 11.2 cos 50 c) 11.2 sin 50 d) infinite 46. Two uniform gold spheres of radius R each exert a gravitational force of F when in contact. The

gravitational force of two uniform gold spheres of radius 2R in contact will be a) F/16 b) F/4 c) F d) 16F 47. The altitude of earth satellite in terms of radius of earth R, when it has a velocity 4km/s is a) R b) 2R c) 3R d) 4R 48. Two forces 100N and 150N act on a body of mass 100 kg. The minimum acceleration this body can

have under their combined action is (in m/s2) a) 3.5 b) 1.5 c) 1.25 d) 0.5 49. A passenger in a car taking a curve feels a centrifugal force on him. This force is a) exerted by car on him b) exerted by ground on him through the car c) the reaction to the centripetal force d) due to inertia 50. The gravitational field at a point at a distance of r from the centre of a uniform sphere of radius R for r

< R is proportional to a) 1/r2 b) 1/r c) r d) r2 51. A particle moving in a horizontal circle of radius r has centripetal force F = -k/r2, where k is a constant.

The kinetic energy of the particle is a) k/r b) k2/r2 c) 2k/r d) k/2r 52. The minimum acceleration with which a fireman can climb down a rope of breaking tension 60% of

his weight is a) 0.4 g b) 0.6 g c) 0.2 g d) 0.3 g 53. ABC is a triangular plate of uniform thickness with sides AB: BC: CA in the ratio 1:3:5. If IAB is the

moment of inertia about AB, IBC that about BC and ICA that about CA, which one of the following is correct ?

a) IBC = IAB b) IAB + IBC = ICA c) ICA is minimum d) IAB < IBC

54. A block takes t seconds to slide down a smooth inclined plane of angle 450. The same block takes 2t seconds to slide down a rough inclined plane of same angle. The coefficient of friction of the second plane is

a) 0.5 b) 1/√2 c) 0.75 d) 1/2√2 55. A heavy nucleus at rest emits can α particle. Then a) momentum of α is greater than that of nucleus b) momentum of nucleus is greater than that of α c) kinetic energy of nucleus is greater than that of α d) kinetic energy of α is greater than that of nucleus 56. A thin uniform needle has a moment of inertia I1 about centre of mass axis. It is bent into a ring. The

moment of inertia is I2 about c.m. then I1 / I2 will be a) π2/3 b) π2/4 c) π2/12 d) 3/π2 57. Assuming earth to be a uniform sphere of density ρ, period of a satellite close to earth is related to the

density by the equation ‘t’ is proportional to a) ρ b) √ρ c) 1/√ρ d) 1/ρ

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5 58. Three forces each of magnitude 1 N act from one corner towards the other three corners of a square.

Their sum has a magnitude nearest to a) 3 N b) 1 N c) 1.4 N d) 2.4 N 59. A laboratory on earth can be taken as a) an inertial frame strictly b) an inertial frame approximately c) a non-inertial frame strictly d) either depending on where we are looking from 60. A particle is falling freely along an inclined plane. It travels the last 1/3 of the distance with 1/nth of

the total time of fall. Here n is nearest to a) 2 b) 3 c) 4 d) 5 61. A car is travelling on a level road of coefficient of static friction 0.8. The car cannot have an

acceleration more than a) 0.8 m/s2 b) 8 m/s2 c) 4 m/s2 d) 10 m/s2

62. A mixture of sea water of specific gravity 1.1 is mixed with fresh water of specific gravity 1. If the mixture has specific gravity 1.04 the ratio of volume of sea water to volume of fresh water is

a) 1:1.04 b) 5:4 c) 5:2 d) 3:2 63. A disc with a small hole is rotating through centre of mass axis with a constant period. If the centre of

the disc is heated the period of rotation will a) increase b) decrease c) remain same d) may increase or decrease 64. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length

vertical, from a fixed point by a mass less spring of force constant k, such that it is half-submerged in a liquid of density ρ at equilibrium position. When the cylinder is given a small downward push and released it oscillates with small amplitude and with a frequency

2/12/12

2/12/1

gAgAk

21)d

MgLk

21)c

MgAk

21)b

MgAk

21)a

⎥⎦

⎤⎢⎣

⎡ρρ−

π⎥⎥⎦

⎤

⎢⎢⎣

⎡ ρ−π

⎥⎦

⎤⎢⎣

⎡ ρ+π⎥⎦

⎤⎢⎣

⎡ ρ−π

65. Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between the planet and the star is proportional to R-5/2, then

a) T2 is proportional to R2 b) T2 is proportional to R7/2

c) T2 is proportional to R3/2 d) T2 is proportional to R3.75

66. *A particle is acted upon by a force is constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that

a) its velocity is constant b) its acceleration is constant c) its kinetic energy is constant d) it moves in a circular path 67. 1 kg of cotton is balanced by 1 kg of a brass weight in a balance covered with a bell jar. If the bell jar

is evacuated, a) the cotton pan will go down b) the brass pan will go down c) both will remain in equilibrium d) cotton will first go up and then come down 68. *A diametrical tunnel is dug along the earth. A particle is dropped from a point at a height h directly

above the tunnel. Assuming earth’s density to be uniform, a frictional forces are negligible, a) the particle reaches the same height on the other side b) the particle will have zero acceleration when it passes through the centre of the earth. c) the particle has maximum acceleration at the point of release d) the particle will oscillate simple harmonically 69. When a running athlete stops after a race a) only his momentum is conserved by himself b) only his kinetic energy is conserved by himself c) both momentum and kinetic energy are conserved by him d) neither momentum nor kinetic energy is conserved by him

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70. A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5 the magnitude of the frictional force acting on the block is

a) 2.5 N b) 0.98 N c) 4.9 N d) 0.49 N 71. A particle of mass m is moving in a circular path of constant radius r such that its centripetal

acceleration ac is varying with time t as ac = k2rt2 where k is a constant. The power delivered to the particle by the forces acting on it is

a) 2πmk2r2t b) mk2r2t c) (mk2r2t5)/3 d) zero 72. One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a massless

spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross section and the Young’s modulus of the wire are A and Y respectively. If the mass is slightly pulled down and released, it will oscillate with a time period T equal to

YAmL2)d

KLmYA2)c

YAK)KLYA(m2)b

Km2)a

ππ

+ππ

73. Among the forces in nature, friction can be classified into a) gravitational b)electro magnetic c) weak nuclear d) strong nuclear 74. When a body covers one quadrant of a circle of radius 0.1 metre, the ratio of distance travelled by it to

the magnitude of displacement is a) 1 b) π/√2 c) π/2 d) π/2√2 75. When a person walks along east, the force of friction is along a) east b) west c) any where from east to west d) anywhere from north to south 76. If distance of earth from sun reduces to half the present value, the number of days in an year would be

nearly a) 730 b) 229 c) 182 d) 130 77. Two bodies of same mass but of different material are released from same height in a medium where

air resistance cannot be neglected. Then a) the denser body reaches ground first b) the less dense body reaches ground first c) both fall through in the same time d) cannot be answered from the data 78. The level of water in a trough when a train is at rest is horizontal. The train starts to move with

uniform acceleration towards right. Then water level will a) still be horizontal b) incline up towards rear of the train c) incline up towards front of the train d) become concave shaped. 79. (Fig) Three equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as

shown in the fig. What is the tension of the string connecting weights B and C ?

A

C

a) 1.3 N b) 1.3 kgwt c) 3.3 N d) 19.6 N 80. If a body moves under constant power, the distance s travelled by it will be

related to the time t by the equation B a) s α t3/2 b) s α t2/3 c) s α t2 d) s α t1/2

81. Two bodies M and N of equal mass are suspended from two separate massless springs of spring constant k1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of amplitude of vibration of M to that of N is equal to

a) 2

1

kk

b)1

2

kk

c) 1

2

kk

1 d)2

1

kk

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7 82. If in the above question, the bodies oscillate so that they have equal maximum acceleration, the

amplitude ratio of M to N is

a) 2

1

kk b)

2

1

kk

c) 1

2

kk

1 d) 1

2

kk

83. *A linear harmonic oscillator of force constant 2 x 106 N/m and amplitude 0.01 m has a total mechanical energy of 160 J. Its

a) maximum potential energy is 100 J b) maximum kinetic energy is 100 J c) maximum potential energy is 160 J d) minimum potential energy is zero 84. A boat which has a speed of 5 km/h in still water crosses a river width 1 km along the shortest possible

path in 15 minutes. The velocity of the river water in km/h is a) 1 b) 3 c) 4 d) 41 85. A particle executes simple harmonic motion of frequency, f. The frequency with which its kinetic

energy oscillates is

a) 2f b) f c) 2f d) 4f

86. A shell is fired from a cannon with a velocity V(m/s) at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the speed (in m/s) of the other piece immediately after the explosion is

a) 2 v cosθ b) 3v cosθ c) 23 v cosθ d)

23 v cosθ

87. The position of a particle at time t, is given by the relation: x(t) = ⎥⎦

⎤⎢⎣

⎡α

0V(1-eαt), where V0 is a constant

and α > 0. The dimensions of V0 and α are, respectively, a) M0L1T0 and T1 b) M0L1T1 and T c) M0L1T-1 and T2 d) M0L1T-1 and T-1

88. In a simple harmonic motion, when the displacement is half the amplitude, what fraction of the total energy is kinetic?

a) 43 b) zero c)

41 d)

21

89. If radius of earth contracts to (1/n)th, with its mass remaining constant, the duration of the day in hour will be

a) 24 b) n24 c) 24 n d) 2n

24

90. A uniform chain of mass M and length L rests on a smooth table with one fourth of its length hanging. the work required to pull the hanging portion is

a) 2

MgL b) 4

MgL c) 16

MgL d)

32MgL

91. When n vectors of different magnitudes are added the sum is zero. Then n cannot be a) 11 b) 6 c) 4 d) 2 92. *In figure, .the spring balance A reads 2 kg with a block m

suspended form it. A balance B reads 5 kg when a beaker with liquid is put on the pan of the balance. The two balances are now so arranged that the hanging mass is inside the liquid in the beaker as shown in fig. In this situation

A

B

a) the balance A will read more than 2 kg b) the balance B will read more than 5 kg c) the balance A will read less than 2 kg and B will read more than 5 kg d) the balances A and B will read 2 kg and 5 kg respectively

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93. The moment of inertia of a thin square plate ABCD, (Fig) of uniform thickness about an axis passing through the centre 0 and perpendicular to the plane of the plate is (where I1, I2, I3, I4 are MI about the axis in its plane)

I1

I2

I3

I4

a) I1 + I2 b) I3 + I4 c) I1 + I3 d) I1 + I2 + I3 + I4

94. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity ω. The force exerted by the liquid at the other end is

a) Mω2 L/2 b) Mω2L c) Mω2L/4 d) Mω2L2/2 95. A car is moving in a circular horizontal track of radius 10m with a constant speed of 10 m/s. A plumb

bob is suspended from the roof of the car by a light rigid rod of length 1.00m. The angle made by the rod with the track is

a) zero b) 300 c) 450 d) 600

96. During a rainstorm, raindrops are observed to be striking the ground at an angle of θ with the vertical. A wind is blowing horizontally at the speed of 5.0 m s-1. The speed of raindrop is (in m/s)

a) 5 sinθ b)θsin

5 c) 5 cosθ d) θcos

5

97. A 2 kg stone at the end of a string 1 m long is whirled in a vertical circle at a constant speed of 4 m s-1. The tension in the string will be 52 N when the stone is

a) at the top of the circle b) halfway down c) at the bottom of the circle d) anywhere on the circle 98. The volume of an air bubble is doubled when it rises from the bottom to the surface of a lake. The

depth of the lake is approximately a) 10 m b) 15 m c) 25 m d) 30 m 99. A body of certain material floats with 9/10 of volume submerged in water in earth. In a planet, where

acceleration due to gravity is five times that of earth, the submerged fraction will be

a) 109 b)

509 c)

1059 d)

2509

100. If the change in the value of g at a height h above the surface of the earth (radius R) is the same as that at a depth x below it (assuming h << R and x <<R), then

a) x = h b) x = 2h c) x =2h d) x =

3h

101. A ass M attached to a light spring oscillates with a period of 2s. If the mass is increased by 2 kg, the eperiod increases by 1 s. the value of M is

m

he a) 1.0 kg b) 2.4 kg c) 2.0 kg d) 1.6 kg 102. T torque produced by a tangential force F, applied to the rim of a disk of radius R will be

a) RF b)

2RF c)

RF d) FR

103. A solid cylinder of radius r rolls down an inclined plane without slipping. The speed of the centre of mass when it reaches the bottom is

gh4)d4gh3

)c3gh4

)bgh2)a

104. A ass m suspended by a strong of length L is executing simple harmonic motion of frequency f. The frequency will become 2f if

m

u

a) the mass m is doubled b) the mass is reduced to m/4 c) the length of the string is reduced to L/4 d) the length is doubled 105. A niform rope lies on a table such that a part of it hangs down the table. When the length of the

hanging part is 1/3 of the entire length, the rope begins to slide. The coefficient of friction between the rope and the table is

a) 21 b)

32 c)

31 d)

61

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b 106. A ucket of water is tied to a rope of length 2.5 m and whirled in a vertical circle. The maximum

period for water not spill from the bucket is (g = 10 m/s2) a) 1 s b) π s c) 2π s d) 2 s 107. The escape velocity of a body on the surface of the earth is 11.2 km/s. The escape velocity at an

altitude 3R, where R is the radius of the earth is (in km/s) a) 22.4 b) 11.2/√3 c) 11.2 x √3 d) 5.6 108. Two satellites A and B each of mass m, are revolving round the earth (of mass M) in a circular orbit of

radius r. The two are moving in opposite direction and hence poised for a collision. On collision the two coalesce to form one body. The total energy of the system after collision is

a) zero b) r

GMm2− c)

r2GMm

− d) r

GMm−

109. The angular velocity with which the earth would have to rotate about its axis so that a person on the equator would feel 3/5 th of his weight is equal to

R3g2

)dR5g3

)cR5g2

)bRg2

)a

110. A re of length L, cross sectional area A and Youngs modulus Y is stretched through a length x. The work done in the process is

wi

a) L

YAx b) L2

YAx c) L

YAx 2 d)

L2YAx 2

111. A issile is launched from moon with a velocity equal to 3km/s. The sum of potential and kinetic energy of the missile will be

m

a) positive b) negative c) could be positive or negative depending on the direction of launch d) zero 112. From a tap water drops are falling at a regular interval of one second. When the fourth drop is

released , first drop reaches the ground. Then distance between third and second drop at the instant of release fo fourth drop is (take g = 10 m/s2).

a) 15 m b) 20 m c) 25 m d) 5 m 113. The dimensions of energy density is same as that of a) pressure b) force c) acceleration d) (velocity)2

114. The error in measuring resistance of a wire is 1%, that in measuring radius 1% and that in length 1%. The error in measuring resistivity of the wire is

a) 0% b) 2% c) 3% d) 4% 115. Which of the following is a not a unit of distance a) fermi b) astronomical unit c) light year d) barn 116. The ratio of linear momentum to angular momentum will have the dimensions of a) velocity gradient b) Rydberg constant c) gravitational field d) force 117. The equation to damping force = constant x velocity. The unit of this constant would be a) kgs-1 b) N c) Nm-2 d) kgs-2

118. In the equation v = a+ bt

ct

+ 2 , where v is velocity , t time, the unit of b is same as that of

a) length b) acceleration c) angle d) area 119. In the equation I = Io(1-e-αt ), I is the current, t, is time. Then the dimension of α is same that of a) current b) time c) angular velocity d) charge 120. Which of the following is a unit of resistivity? a) VA-1 b) VAm-1 c) VA-1m-1 d) VA-1m 121. The dimension of a quantity whose unit is `torr’is a) ML-1T-2 b) MLT-2 c) LT-2 d) LT-1 122. The volume of a cube in m3 is equal to its surface area in m2. Then the volume in m3 is equal to a) 1000 b) 100 c) 216 d) 1

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123. The distance travelled by the body during nth second is given by Sn = u+a(n- 12

). The dimensions of

Sn here is a) L1 b) LT-1 c) T-1 d) LT-2

124. If R is resistance V potential, t time, R-1 tV2 has the dimensions of a) energy b) power c) (current)2 d) electric field 125. The pair which does not have same dimension is a) curie and frequency b) angular velocity and velocity gradient c) coefficient of friction and Reynold’s number d) torque and angular momentum 126. Which of the following has units but no dimensions? a) frequency b) solid angle c) gravitation constant d) Planck’s constant 127. If force F, length L, and time T are assumed as fundamental quantities, the dimensional formula for

mass will be a) FL-1T2 b) FL-1T-2 c) FLT-2 d) FLT2

128. The dimension of gravitational field is same as that of a) force b) velocity c)acceleration d) momentum 129. kg m-1s-1 is the unit of a) momentum b) viscosity c) surface tension d) stress 130. E, M, J and G denote energy, mass, angular momentum and gravitation constant respectively. The

dimensions of EJ2/M5G2 are that of a) time b) length c) mass d) angle 131. If η is modulus of rigidity, L length, M mass, which of the following will have dimensions of period? a) M Lη b) L/Mη L/M)d/ML)c ηη

132. A body released from the top of a tower falls through a height of 5 m during the first second of its fall and 35 m during the last second of its fall. The height of the tower is

a). 80 m b) 60 m c) 40 m d) 20 m 133. An electric train starts from a station A, accelerates for 20 s and reaches a speed of 20 m/s, travels with

that speed for next 5 minutes and stops within the next 20 seconds at the station B. The distance between the stations A and B will be

a) 6800 m b) 3400 m c) 6000 m d) 6400 m 134. The equation to the motion of a body can be written as x = at3+bt2+ct+d, where a,b,c,d are positive

constants. This body has a) Uniform acceleration b) Uniform retardation c) Uniformly increasing acceleration d) Non-uniform and irregular acceleration 135. A cyclist running down a slope takes 2 minutes to reach the bottom of the slope. The time to cover

first 1/4th of the slope will be (in minutes) a) 1 b) 1.4 c) 0.7 d) 0.5 136. A boat takes t seconds to cover a river when travelling down stream and 3 times of that time to travel

upstream. The ratio of speed of boat to speed of river current is a) 3:1 b) 2:1 c) 4:1 d) 3:2 137. Check which of the following statement is wrong : a) a body can have eastward velocity and westward acceleration. b) a body can have increasing speed and decreasing acceleration c) a body can have uniform velocity and uniform acceleration. d) a body can have zero velocity and acceleration 138. A stone falling freely covers during the last second distance equal to that in first three seconds. The

time of fall is equal to a) 4 s b) 4. 5 s c) 5 s d) 6 s 139. The distance time graph of a body dropped from the top of a tower will be a) a straight line of positive slope through origin b) a straight line of positive slope not through origin c) a parabola but not passing through origin d) a parabola through origin

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11 140. The speed of a body x moving with uniform acceleration is doubled in covering a distance of y m.

When it covers an additional distance y, its speed would become a) 3x b) 4x c) 6 x d) 7 x 141. A stone falls through a certain height in earth in 2 seconds . In moon where acceleration to gravity is

1/6 of that of earth, it will fall the same height in ( seconds) a) 2 b) 24 c) 12 d) 2 3/

142.A body starts from rest with uniform acceleration a. Its velocity after n second is v. The displacement of body in the last two seconds is

n2)1n2(v)d

n)1n(v)c

n)1n(v).b

n)1n(v2)a ++−−

143. A bullet strikes a uniform wooden plank with a speed x and emerges with a speed y. If the plank had only half the thickness, the bullet would have emerged with a speed

a) 2 y b) 2y c) ( )x y2 2 2+ / d) (x+y)/2 144. Two bodies A and B are projected with same initial velocity from a point. They travel same horizontal

distance. If the angle of projection of A is α, then the ratio of maximum height of A to that of B is a) sin2α b) sin α c) tan2α d) tan α 145. A projectile is fired with an initial momentum p at an angle 600 to the horizontal. The change in

momentum when it strikes the ground is a) 0 b) p/2 c) ( 3 /2) p d) p 146. The path of a projectile as seen from another projectile will be a) a straight line b) a parabola c) an arc of circle d) an irregular curve 147. A particle moves in a plane with a constant acceleration in a direction different from the initial

velocity. The path of the particle will be a) a straight line b) an arc of a circle c) a parabola d) an ellipse 148. In the arrangement shown in Fig. the ends of P and Q of an

unstretchable string move downwards with speed u. The pulleys are fixed. Mass M moves upwards with speed of:

a) 2ucosθ b) u/ cos θ c) 2u/cos θ d) ucos θ 149. Given vector as A i the angle between it and y-axis is : j= +2 3 , a) tan-1 (3/2) b) tan-1 (2/3) c) sin-1 (2/3) d) cos-1 (2/3)

150. The velocity vector of a certain uniform circular motion is given by v a i b= + j . The acceleration vector will be

ibja)djbia)cibja)bjbia)a −++− 151. A particle is moving eastwards with a velocity 10 m/s. In 10s the velocity changes to 10 m/s

northwards. The average acceleration during this time is a) 0 b) 1/ 2 ms-2 N-E c) 2 ms-2N-W d) 1/2 ms-2 N-W 152. A body is projected from the top of a tower with a constant force in the horizontal direction. The path

of the body will be a) a parabola b) a straight line c) an arc of a circle d) an irregular curve 153. A stone is tied to one end of a string of length 1 m fixed at the other end . It is projected horizontally

with a velocity 6 m/s so that it moves in vertical plane. Then a) the stone will complete a vertical circle b) the stone will reach maximum height and fall down c) the stone will follow a parabolic path d) the stone will move in a horizontal straight line 154. A particle is moving in a circle with a velocity v as shown in fig. The

change in velocity when it moves between two points is a) 2 v cos 100 b) 2 v sin 100 c) 2 v cos 200 d) 2 v sin 200

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155. N coplanar force vectors each of length x act such that each vector makes an angle 2π / N radian with the preceding vector. The sum of these vectors will be

a) Nx b) x c) 2x(N-1)/N d) 0 156. The sum of (N-1) force vectors in question 12 has a magnitude a) (N-1)x b) (N-1)x/2 c) x d) 0 157. If t1 and t2 are the times of flight of a projectile for two angles to obtain same horizontal range, then t1t2

= a) 2R/g b) R/g c) R/2g d) 4R/g Solve the following two problems within a maximum time of 2minutes. Use only one equation. 158. A body A is projected with a velocity 20 m/s from the bottom of a tower of height 40 m. At the same

time a body B is projected down with same velocity 20 m/s down ward in the same line. Find after what time the bodies meet.

159. Two runners are initially at a distance of 8 metre at rest. They start at the same time with front runner accelerating at 3 m/s2 and back runner 4 m/s2. After what time the back runner overtakes the front runner ?

160. A body of mass m projected from lowest point just completes a vertical circle of radius r . Its total energy is

a) (1/2)mgr b) mgr c) (3/2)mgr d) (5/2)mgr 161. A rope has breaking tension 0.4 of the weight of the climber. In which of the following case the rope

will not break ? a) when the climber accelerates up with 0.6 g b) when the climber accelerates up with 0.4 g c) when climber accelerates down with 0.6 g d) when climber accelerates down with 0.4 g 162. The bridge over a river is in the form of an arc of radius 5 m. What is the safest velocity of a motor

cyclist at the highest point of the bridge? a) 7 m/s b) 5 m/s c) 9.8 m/s d) 4.9 m/s 163. Which of the following statement(s ) is/are correct in the case of electron going around the nucleus of

an atom? a) centripetal force is provided by electrostatic force of attraction. b) The centrifugal force on the electron is balanced by the above electrostatic force of attraction. c) If the centripetal force vanishes, the electron will be thrown off outwards due to the centrifugal force. d) If nuclear attraction ceases, the electron will take off in a straight line. 164. (Fig.) A body falling from a height h just completes a vertical circle of diameter AB=D as shown in

figure. Then h = a) D b) D/2 c) (5/4)D d) (2/5)D 165. A body having a kinetic energy of 100 J explodes into two pieces of

masses in the ratio 3:2. The kinetic energy of larger piece will be (in J) a) 60 b) 40 c) 50 d) 60x 3 2/ 166. A body moves so that distance travelled s α t3/2. This body has a) constant force acting on it b) constant kinetic energy c) constant power d) all the above three constant

167. A sharp screw driver of mass M is dropped from a height h on a wooden floor . If the screw penetrates x metre into wood, the average resistance offered by the wood to the screw is

a) Mg b) ⎥⎦⎤

⎢⎣⎡ +

xh1Mg c) ⎥⎦

⎤⎢⎣⎡ −

xh1Mg d)

2

xh1Mg ⎥⎦⎤

⎢⎣⎡ +

168. An impulse is supplied to a moving object with the force at an angle of 1200 with respect to velocity vector. The angle between the impulse vector and the change in momentum vector is

a) 1200 b) 00 c) 600 d) 2400

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169. A body of mass 4 kg explodes into 3 pieces 1 kg, 1 kg and 2 kg. One 1 kg and 2 kg move at right angles with speeds 2 m/s and 1 m/s respectively. The speed of the other mass is

a) 2 m/s b) 1 m/s c) √3 m/s d) √8 m/s 170. A ball falls through a certain height and after n rebounds raises to (1/n)th of the original height, where

n is an integer greater than 1. The coefficient of restitution of the surface is a) 1/n b) 1/n2 c) 1/√n d) (1/n) 1/2n

171. When kinetic energy of a body is reduced to half , the momentum decreases by a) 50% b) 41% c) 71% d) 29%

172. *Three coplanar forces 1,2,3 N act on a body of mass 1 kg. Which of the following statement (s) is/are correct ?

a) the body can be in equilibrium as the forces can form sides of a triangle. b) the body can be in equilibrium although the forces cannot form sides of a triangle. c) the body cannot have an acceleration more than 6 m/s2

d) the body can have an acceleration 3.15 m/s2. 173. A horizontally connected system with one mass hanging freely and one mass on the table, has an

acceleration (1/8)g. The ratio of the masses is a) 7 b) 6 c) 8 d) 4

174. A force F produces an acceleration a on a body. If two such forces act at the same body at the same time at an angle 120o it will have an acceleration

a) 2a b) a c) a/√2 d) √2a 175. A force of 1N acts on a body of weight 1N. The acceleration produced on the body is (in m/s2) a) 1 b) 9.8 c) 1/9.8 d) 4.9

176. A body of mass 4 kg moves along the X-axis with a speed 1.5 m/s. A force of 4N is applied along the Y-axis. The distance of the body from the origin after 4 s will be

a) 20 m b) 14 m c) 10 m d) 5 m 177. A body of mass 20 kg at rest is acted on by 10 N force for 3 s and then 20 N force for 4 s and then 30

N force for 5 s in the same direction.. The velocity of the body now would be (in m/s) a) 13 b) 10/3 c) 20/3 d) 26

178. A body at rest on a rough horizontal surface starts with an acceleration when a force f is applied. When the force is doubled, the acceleration increases to 4 times. The force necessary just to start the body will be

a) f b) 2f c) f/2 d) 2f/3 179. A constant force of 20N acting on the body makes it to move with a constant velocity 10 m/s at an

angle 30 degrees with the force. The power developed by the body in W is a) 200 b) 100 c) 100√3 d) 400/√3

180. The string of a conical pendulum will become horizontal when a) its speed of revolution is infinite b) its speed of revolution is zero c) its speed of revolution is low but not zero d) speed of revolution is high but not infinite

181. Three bodies of masses in the ratio 1:2:3 have equal momentum. Their kinetic energy will be in the ratio

a) 1:2:3 b) 3:2:1 c) 1:4:9 d) 6:3:2 182. A can filled with water is revolved in a vertical circle of radius 4 m so that water does not just fall

down at the highest point . The time period of revolution of the can is (Take g = π2 ) a) 8 s b) 4 s c) 2 s d) 1 s

183. A spring stretched by ‘x’ has a potential energy U . If it is stretched by 2x more, the increase in potential energy due to second stretching is

a) 2U b) 4U c) 6U d) 8U 184. When a train moves with a speed of 30 km/h, frictional force on it is 10N/100 kg. Check the correct

statement(s): a) When the speed increases to 60 km/h ,the frictional force is doubled b) When the speed increases to 60 km/h ,the frictional force becomes 4 times c) During increase of speed from 30 to 60 the frictional force will increase d) the frictional force will be same at 30 and 60 km/h

185. A bullet of mass m moving at a speed of v strikes on a block of mass 2m suspended by a string and gets embedded in it. If the block rises through a height h the speed of the bullet is

a) gh2 b) gh3 c) gh6 d) gh2

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186. The same force is applied to bodies of different masses . If the accelerations are plotted with their respective masses the correct graph will be

a) 1 b) 2 c) 3 d) 4

187. A body falling from a height strikes a surface with a speed v. If it loses 10% of its kinetic energy after each impact, its velocity after second impact will be

a) 0.9 v b) 0.8 v c) 0.81 v d) 0.6 v 188. Two spheres of masses 2 kg and 1 kg moving with velocity 4 m/s and 2 m/s respectively collide

inelastically . If e = 0.5, the loss of kinetic energy after collision is a) 6 J b) 3J c) 1.5J d) 1 J

189. A lorry requires a minimum stopping distance of s, when it has a momentum p. When it has a momentum 2p the stopping distance would be

a) s b) 2s c) 1.4s d) 4s 190. Two balls having same initial energy are projected, one vertically up and the other at an angle of 300

to the horizontal Their potential energy at the highest point will be in the ratio a) 4:3 b) 3:4 c) 4:1 d) 1:4

191. The balls having the same initial of kinetic energy are projected at angles 300 and 600. The ratio of their kinetic energy at highest point will be

a) 4:3 b) 3:4 c) 4:1 d) 3:1 192. A coin falls vertically from a height to a surface of coefficient of restitution e = 0.5. The energy lost at

the first rebound as percentage of original energy is a) 25 b) 50 c) 75 d) 80

193. A force produces an acceleration a1 on a body of mass m1 and an acceleration a2 on a body of mass m2. Then the acceleration produced by the same force on combined mass m1+m2 will be

a) a1+a2 b) (a1+a2 )/2 c) √a1a2 d) a1a2/ a1+a2

194. A freely falling body loses gravitational potential energy U and attains a velocity v. The mass of this body is

a) 2U/v2 b) U/ v2 c) (U)/ 2v2 d) 2√U/v 195. A shell has a kinetic energy E . During flight it explodes into a number of small pieces. Then the sum

of kinetic energies of all these pieces will be a) E b) less than E c) more than E d) 0

196. A body of mass 1 kg has a velocity 3 . Its kinetic energy in J is equal to 4i + j a) √50 b) 50 c) 25 d) 12.5

197. Assume air resistance to the motion of a rocket is proportional to square of its speed at initial stages. The ratio of power required at a speed 4 km/s to that required at a speed 8 km/s is

a) 1:1 b) 1:2 c) 1:4 d) 1:8 198. * Imagine a diametrical tunnel dug across earth. A body is dropped into this tunnel. Ignore friction

and other dissipative forces. Check which of the following statements are correct: a) the acceleration of the body will be zero at the centre of earth. b) velocity of the body will be zero at the centre of the earth c) kinetic energy of the body will be maximum at the centre of earth d) potential energy will be zero at the centre of earth

199. A simple pendulum of length l has a bob of mass M. If the string is displaced through an angle θ, the potential energy attained will be equal to

a) Mgl cosθ b) 2Mgl sin2(θ/2) c) 2Mgl cosθ d) 2Mgl cos2(θ/2) 200. Two cars A and B having equal momentum collide head on. In the process a) heavier car suffers greater damage b) lighter car suffers greater damage c) both suffer same damage d) cannot be answered from the data

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201. A particle strikes at an angle 300 with X-axis with a speed v and rebounds with the same speed at the same angle as shown . The change in momentum of this particle will be a) mvi b) 2mvi

c) mvj d) 2mvj 202. A body of mass m is projected at a certain angle has a time of flight T. When it strikes ground the

change in momentum is equal to a) mg T b) mg T/2 c) 2mg T d) 0

203. A body of weight W rests on a rough horizontal surface of angle of friction λ . The minimum force that will start motion of this body along the surface is

a) W sin λ b) W cos λ c) W d) W tan λ 204. The angle between force of friction and instantaneous velocity of a body when it just starts is equal to a) 0 b) 180 c) 90 d) any angle

205. A spring of mass M and length L(stiffness constant K) is compressed vertically downward against the floor so that its compressed length becomes L/2. On releasing it, the work done by it on the floor is

a) 2mKL21 b)

2

2LK

21

⎥⎦⎤

⎢⎣⎡ c) zero d) KL2

206. * Which of the following has/have the dimensions of power? a) force x distance b) force x velocity c) torque x distance d) torque x angular velocity

207. Two blocks A and B of masses 5 kg and 3 kg respectively rest on a smooth horizontal suface as shown is fig. If coefficient of friction between A and B is 0.5, then the maximum horizontal force kg wt which can be applied to A so that A and B move without separation is

a) 2 b) 3 c) 4 d) 5

208. A ball is thrown down so that it will rebound 10 m higher than the original level. The speed of the throw is

a) 5 m/s b) 14 m/s c) 20 m/s d) 14√2 m/s

209. The power supplied by a force acting on a particle moving in a straight line is constant. The velocity of the particle varies with the displacement x as

a) √x b) x c) x2 d) x1/3

210. * A force F acts on a body of mass 1 kg moving with an initial velocity vo for 1 s. Then the a) distance covered by the body is vo + (F/2) b) change in kinetic energy of the body is (1/2) mF2

c) final velocity of the body is vo+F d) momentum of the body increases by F

211. *A body is revolving with a constant speed along a circular path. If the direction of its velocity is reversed, keeping speed unchanged, then

a) the centripetal force does not suffer any change in magnitude b) the centripetal force does not suffer any change in direction c) the centripetal force will have its direction reversed d) the centripetal force will be doubled

212. *A reference frame attached to the earth a) is an inertial frame by definition b) cannot be an inertial frame because the earth is revolving round the sun c) is an inertial frame because Newton’s laws are applicable in this frame d) cannot be an inertial frame because the earth is rotating about its own axis.

213. A cord is used to lower vertically a block of mass M through a distance d at a constant downward acceleration of g/4. Then the work done by the cord on the block is

a) Mg d/4 b) 3Mgd/4 c) -3Mgd/4 d)-mgd/4 214. Two particles of masses 1 kg and 3 kg move towards each other under their mutual force of attraction.

No other force acts on them. When the relative velocity of approach of the two particles is 2 m/s, their centre of mass has a velocity of 0.5 m/s. When the relative velocity of approach becomes 3 m/s the velocity of centre of mass is

a) 0.75 m/s b) 0.5 m/s c) 2.5 m/s d) 0 m/s

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215. A body is projected with a velocity just equal to escape velocity. Its kinetic energy plus potential energy is

a) positive b) negative c) zero d) cannot be said from the data

216. A wheel starting from rest with uniform angular acceleration rotates through 30 radian in second second. In the third second it will rotate through an angle

a) 30 radian b) 45 radian c) 50 radian d) 60 radian 217. A body of mass 2 kg has a velocity vector v =5i and a position vector r =12 .j Its angular

momentum with respect to the origin is a) 120 units along negative z axis b) 120 units along positive z axis c) 60 units along positive z axis d) 60 units along negative z axis

218. A light metre scale carries a 1 kg mass at zeroeth division and a mass of 3 kg at 100th division. If this scale is to be rotated with minimum torque with constant angular acceleration, the axis of rotation should pass through

a) 30th division b) 50th division c) 66.6th division d) 75th division 219. Three wheels of moments of inertia in the ratio 1:2:3 rotate with same kinetic energy. They are

stopped by equal torques. The angle of rotation before they come to rest will be in the ratio a) 1:2:3 b) 3:2:1 c) 6:3:2 d) 2:3:6

220. A ball moving with constant speed u hits another ball of the same mass at rest. The coefficient of restitution is e. The ratio of the velocities of two balls after the collision is

a) e b) 1+e c) 1-e d) (1-e)/(1+e) 221. A solid sphere rolls forward . The ratio of its kinetic energy of translation to total energy is equal to a) 2/7 b) 2/5 c) 5/7 d) 2/3

222. Three particles A,B and C of equal masses move with equal speeds v each from corners along the medians of an equilateral triangle. They collide at the centroid G of the triangle. After the collision A comes to rest, B retraces its path with the speed v. The velocity and direction of C is

a) (v/2) in the direction of B b) v opposite direction of the B c) v in the direction of B d) retrace of its path with same velocity

223. The moment of inertia of a cylinder about an axis through its centre of mass perpendicular to its plane is equal to that about its natural axis. The ratio length of the cylinder to radius of the cylinder is

a) 2 b) 3 c) √2 d) √3 224. Two fly wheels of same size but of different mass have same angular momentum. Then a) the lighter one has greater kinetic energy of rotation. b) the heavier one has greater kinetic energy of rotation c) both have same kinetic energy of rotation d) cannot be answered from the data

225. From a thin uniform wire two circular loops of radii in the ratio 1:2 are formed. If the loops are rotated about an axis through centre of mass perpendicular to the plane, the ratio moment of inertia of bigger loop to smaller loop is

a) 8 b) 4 c) 2 d) 16 226. The orbital speed of a geo- stationary satellite, assuming circular orbit is nearly a) 0.5 km/s b) 3 km/s c) 5 km/s d) 8 km/s

227. If the orbital radius of an earth satellite increases by 2 % its period of revolution increases by a) 0.66% b) 1.66% c) 2% d) 3%

228. If the magnitude of the total energy of an earth satellite decreases by 1% its time period of revolution a) will increase by 1% b) will decrease by 1% c) will increase by more that 1% d) will decrease by more than 1%

229. If angular velocity of earth increases to n times the present value, a person at equator feels weightlessness. Here n is nearest to

a) 2 b) 8 c) √17 d) 17 230. If the radius of earth decreases by 1% with density remaining the same, the acceleration due to gravity

on the surface will a) decrease by 1% b) increase by 1% c) decrease by 2% d) increase by 2%

231. A geo-stationary satellite is orbiting the earth at a height of 6R above the surface of earth, R being radius of earth. The time period of another satellite at a height of 2.5R from the surface of earth is

a) 6√2 h b) 6 h c) 6/√2 h d) 10 h

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17 232. The masses and radii of earth and moon are m1, R1 and m2, R2 respectively. Their centres are a

distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway between the two centres so as to escape to infinity is

a) 2

21 2 1 2G m md

bG m m

d( )

)( )+ +

c) G m m

dd

G m md

( ))

( )1 2 1 2

2+ +

233. A satellite is orbiting very close to earth. The minimum percentage increase in velocity that should be given to it so that it escapes from earth’s field is

a ) 41 b) 71 c) 100 d) 141 234. The melting of polar ice caps of earth a) will increase the duration of the day b) will decrease the duration of the day c) will not affect the duration of the day d) will increase or decrease the duration of the day depending on the season

235. *A body of weight 100 N on earth is taken to moon. Take acceleration due to gravity in moon to be (1/5)th of that of earth. Check the correct statement(s):

a) The weight of the body will go on decreasing until it reaches 20 N in moon. b) The weight of the body will be zero at midway between earth and moon. c) The weight of the body will be zero at a point somewhere nearer to moon than earth. d) The mass of the body will remain constant throughout.

236. Imagine a hypothetical planet whose escape velocity is five times that of earth. In this planet a) all lighter gases will be present, heavier ones will be absent. b) all heavier gases will be present and lighter ones will be absent. c) all gases will be present d) all gases will be absent.

237. The period of an earth satellite will not depend on a) mass of earth b) distance of the satellite c) gravitation constant d) mass of the satellite

238. Two missiles A and B are launched with same velocity 4 km/s, A from earth and B from moon. The sum of their potential and kinetic energy will be

a) negative for B and positive for A b) positive for B and negative for A c) positive for both A and B d) negative for both A and B

239. The ratio of gravitational field inside a uniform solid sphere at distances r1 and r2 from its centre E1/E2 is

a) r12/r2

2 b) r22/r1

2 c) r2/r1 d) r1/r2 240. A body is dropped from a height R (radius of earth) from the surface of earth. The velocity with

which it strikes earth is

gR2)d2

gR)cgR)bgR2)a

241. If earth were to rotate with a period T, a person in equator feels half of his weight. Here T is (in minutes)

a) 84 b)168 c) 84x√2 d) 168x√2 242. The work done in moving a unit mass from the surface of a planet to 10 m above is 100 J. The

gravitational field due to this planet at this point is (in N/kg) a) 10 b) 50 c) 100 d) 0

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SECTION 2: ANSWERS 1 (c) 2 (d) 3 (c) 4 (c) 5 (b)

6 (a) 7 (d) 8 (d) 9 (c) 10 (d)

11 (d) 12 (b) 13 (c) 14 (d) 15 (a)

16 (c) 17 (d) 18 (c) 19 (c) 20 (b)

21 (b) 22 (c) 23 (a) 24 (d) 25 (a)

26 (c) 27 (a) 28 (d) 29 (b) 30 (c)

31 (b) 32 (b) 33 (b) 34 (c) 35 (d)

36 (b) 37 (d) 38 (a) 39 (c) 40 (b)

41 (c) 42 (d) 43 (b) 44 (d) 45 (a)

46 (d) 47 (c) 48 (d) 49 (d) 50 (c)

51 (d) 52 (a) 53 (c) 54 (c) 55 (d)

56 (a) 57 (c) 58 (d) 59 (d) 60 (d)

61 (b) 62 (d) 63 (a) 64 (b) 65 (b)

66 (c),(d) 67 (a) 68 (a),(b) 69 (d) 70 (b)

71 (b) 72 (b) 73 (b) 74 (d) 75 (a)

76 (d) 77 (a) 78 (c) 79 (b) 80 (a)

81 (b) 82 (c) 83 (c),(d) 84 (b) 85 (a)

86 (b) 87 (d) 88 (a) 89 (d) 90 (d)

91 (d) 92 (b),(c) 93 (a),(b),(c) 94 (a) 95 (b)

96 (b) 97 (c) 98 (a) 99 (a) 100 (b)

101 (d) 102 (d) 103 (b) 104 (c) 105 (a)

106 (b) 107 (d) 108 (d) 109 (d) 110 (d)

111 (a) 112 (a) 113 (a) 114 (d) 115 (d)

116 (b) 117 (a) 118 (a) 119 (c) 120 (d)

121 (a) 122 (c) 123 (b) 124 (a) 125 (d)

126 (b) 127 (a) 128 (c) 129 (b) 130 (d)

131 (d) 132 (a) 133 (d) 134 (c) 135 (a)

136 (b) 137 (c) 138 (c) 139 (d) 140 (d)

141 (b) 142 (a) 143 (c) 144 (c) 145 (d)

146 (a) 147 (c) 148 (b) 149 (b) 150 (d)

151 (c) 152 (b) 153 (c) 154 (b) 155 (d)

156 (c) 157 (a) 158 1 s 159 4 s 160 (d)

161 (c) 162 (a) 163 (a),(d) 164 (c) 165 (b)

166 (c) 167 (b) 168 (b) 169 (d) 170 (d)

171 (b) 172 (b),(c),(d) 173 (a) 174 (b) 175 (b)

176 (c) 177 (a) 178 (d) 179 (c) 180 (a)

181 (d) 182 (b) 183 (d) 184 (c),(d) 185 (c)

186 (d) 187 (a) 188 (d) 189 (d) 190 (d)

191 (d) 192 (c) 193 (d) 194 (a) 195 (c)

196 (d) 197 (d) 198 (a),(c),(d) 199 (b) 200 (b)

201 (b) 202 (a) 203 (d) 204 (a) 205 (c)

206 (b),(d) 207 (c) 208 (b) 209 (d) 210(a),(c),(d)

211 (a),(b) 212 (b),(d) 213 (b) 214 (b) 215 (c)

216 (c) 217 (a) 218 (d) 219 (d) 220 (d)

221 (c) 222 (b) 223 (d) 224 (a) 225 (a)

226 (b) 227 (d) 228 (c) 229 (d) 230 (a)

231 (a) 232 (b) 233 (a) 234 (a) 235 (c),(d)

236 (c) 237 (d) 238 (b) 239 (d) 240 (b)

241 (c) 242 (a)