PhysicsFlame Institute - Part 36

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106. A circular disc has a mass of 1 kg and radius 40 cm. It is rotating about an axis passing through its centre and perpendicular to its plane with a speed of 10 rev/s. The work done in joules in stopping it would be

(a) 4 (b) 47.5 (c) 79 (d) 158 Ans. d (17)

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105. A solid sphere of mass 1 kg rolls on a table with linear speed 1 m/s. Its total kinetic energy is

(a) 1 J (b) 0.5 J (c) 0.7 J (d) 1.4 J Ans. c (5)

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103. The ratio of kinetic energies of two spheres rolling with equal centre of mass velocities is 2 : 1. If their radii are in the ratio 2 : 1; then the ratio of their masses will be

(a) 2:1 (b) 1:8 (c) 1:7 (d) 2√2:1 Ans. a (12)

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102. A disc of radius 1m and 4 kg mass rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of 10 cm/s Its rotational kinetic energy is

(a) 0.01 erg (b) 0.02 joule (c) 0.03 joule (d) 0.01 joule Ans. d (49)

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101. The speed of rolling of a ring of mass M changes from V to 3V. What is the change in its kinetic energy

(a) 3MV2 (b) 4MV2 (c) 6 MV2 (d) 8MV2 Ans. d (392)

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99. Ratio of kinetic energy and rotational energy in the motion of a disc is

(a) 1 : 1 (b) 2 : 7 (c) 1 : 2 (d) 3 : 1 Ans. d (9)

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98.

A body of moment of inertia of 3kg-m2 rotating with an angular speed of 2 rad/sec has the same kinetic energy as a mass of 12 kg moving with a speed of (a) 1 m/s (b) 2 m/s (c) 4 …

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92.

The moment of inertia of a body about a given axis is 2.4 kg–m2. To produce a rotational kinetic energy of 750 J, an angular acceleration of 5 rad/s2 must be applied about that axis for (a) 6 sec (b) …

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If it is assumed that the spinning motion of earth increases, then the weight of a body on equator

(a) Decreases (b) Remains constant (c) Increases (d) Becomes more at poles Answer: a (3)

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90.

In a bicycle the radius of rear wheel is twice the radius of front wheel. If rF and rr are the radii, vF and vr are speeds of top most points of wheel, then (a) vr = 2 vF (b) vF = …

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85.

A smooth sphere A is moving on a frictionless horizontal plane with angular speed ω and center of mass with velocity v . It collides elastically and head-on with an identical sphere B at rest. Neglect friction everywhere. After the collision, …

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69.

If I1 is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its centre of mass, and I2 is the moment of inertia of the ring formed by bending the rod, …

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67.

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia …

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A body of mass m rises to height h = R/5 from the earth’s surface, where R is earth’s radius. If g is acceleration due to gravity at earth’s surface, the increase in potential energy is

(a) mgh (b) 4/5 mgh (c) 5/6 mgh (d) 6/7 mgh Answer: c (12)

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97. A body is rolling without slipping on a horizontal plane. If the rotational energy of the body is 40% of the total kinetic energy, then the body might be

(a) Cylinder (b) Hollow sphere (c) Solid cylinder (d) Ring Ans. b (12)

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96. A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

(a) 2/5 (b) 2/7 (c) 3/5 (d) 3/7 Ans. b (3)

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The gravitational field due to a mass distribution is E = K/x3 in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is

(a) K/x (b) K/2x (c) K/x2 (d) K/2×2 Answer: d (4)

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95. A thin hollow cylinder open at both ends:

(i) Slides without rotating (ii) Rolls without slipping, with the same speed. The ratio of kinetic energy in the two cases is (a) 1 : 1 (b) 4 : 1 (c) 1 : 2 (d) 2 : 1 Ans. c …

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94. The ratio of rotational and translatory kinetic energies of a sphere is

(a) 2/9 (b) 2/7 (c) 2/5 (d) 7/2 Ans. c (8)

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In a gravitational field, at a point where the gravitational potential is zero

(a) The gravitational field is necessarily zero (b) The gravitational field is not necessarily zero (c) Nothing can be said definitely about the gravitational field (d) None of these Answer: a (22)

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If earth is supposed to be a sphere of radius R, if g30 is value of acceleration due to gravity at latitude of 30o and g at the equator, the value of g – g30°is

(a) ( 1/4 ) ω2R (b) (3/4)ω2R (c) ω2R (d) (1/2 …

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93. A solid sphere of mass 500 gm and radius 10 cm rolls without slipping with the velocity 20cm/s. The total kinetic energy of the sphere will be

(a) 0.014 J (b) 0.028 J (c) 280 J (d) 140 J Ans. a (42)

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Acceleration due to gravity ‘g’ for a body of mass ‘m’ on earth’s surface is proportional to (Radius of earth=R, mass of earth=M)

(a) GM/R2 (b) m0 (c) mM (d) 1/R3/2 …

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A body has a weight 90 kg on the earth’s surface, the mass of the moon is 1/9 that of the earth’s mass and its radius is 1/2 that of the earth’s radius. On the moon the weight of the body is

(a) 45 kg (b) 202.5 kg (c) 90 kg (d) 40 kg Answer: d (4)

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The masses of two planets are in the ratio 1 : 2. Their radii are in the ratio 1 : 2. The acceleration due to gravity on the planets are in the ratio

(a) 1 : 2 (b) 2 : 1 (c) 3 : 5 (d) 5 : 3 Answer: b (7)

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If M the mass of the earth and R its radius, the ratio of the gravitational acceleration and the gravitational constant is

(a) R2/M (b) M/R2 (c) MR2 (d) MR Answer: b (3)

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80. The earth E moves in an elliptical orbit with the sun S at one of the foci as shown in the figure. Its speed of motion will be maximum at the point

(a) C (b) A (c) B (d) D Ans. b (8)

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At what depth below the surface of the earth, acceleration due to gravity g will be half its value 1600 km above the surface of the earth

(a) 4.2 ×106 m (b) 3.19 × 106 m (c) 1.59 ×106m …

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Two planets of radii in the ratio 2 : 3 are made from the material of density in the ratio 3 : 2. Then the ratio of acceleration due to gravity g1/g2 at the surface of the two planets will be

(a) 1 (b) 2.25 (c) 4/9 (d) 0.12 Answer: a (6)

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If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that of the earth, the gravitational acceleration on the surface of that planet is

(a) 0.2 g (b) 0.4 g (c) 2 g (d) 4 g Answer: a (7)

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A body weight 500 N on the surface of the earth. How much would it weigh half way below the surface of the earth

(a) 125 N (b) 250 N (c) 500 N (d) 1000 N Answer: b (5)

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What should be the angular speed of earth, so that body lying on equator may appear weightlessness ( g = 10 m/s2, R=6400 km )

(a) 1/800 rad/s (b) 1/400 rad/s (c) 1/600 rad/s …

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A person will get more quantity of matter in kg –wt. at

(a) Poles (b) At latitude of 60o (c) Equator (d) Satellite Answer: d (12)

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89. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be

(a) K2/R2 (b) K2/K2+R2 (c) R2/K2+R2 (d) K2+R2/R2 Ans. b (5)

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87. A stick of length l and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in the figure. If after the collision ball comes to rest, then what should be the mass of the ball

(a) m=2M (b) m=M (c) m=M/2 (d) m=m/4 Ans. d (10)

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A cubical block of side α is moving with velocity v on a horizontal smooth plane as shown. It hits a ridge at point O. The angular speed of the block after it hits O is

(a) 3v/4a (b) 3v/2a (c) √3v/√2a (d) Zero Ans. a (4)

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84. A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω . Another disc of same dimension but of mass M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is

(a) 2ω/5 (b) 2ω/√5 (c) 4ω/5 (d) 4ω/√5 Ans. c (14)

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82. A uniform disc of mass M and radius R is rotating about a horizontal axis passing through its centre with angular velocity ω. A piece of mass m breaks from the disc and flies off vertically upwards. The angular speed of the disc will be

(a) (M-2m)ω/(M-m) (b) (M+2m)ω/(M+m) (c) (M-2m)ω/(M+m) (d) (M+2m)ω/(M-m) Ans. a (154)

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91. The total kinetic energy of a body of mass 10 kg and radius 0.5 m moving with a velocity of 2 m/s without slipping is 32.8 joule. The radius of gyration of the body is

(a) 0.25 m (b) 0.2 m (c) 0.5 m (d) 0.4 m Ans. d (37)

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88. In a playground there is a merry-go-round of mass 120 kg and radius 4 m. The radius of gyration is 3m. A child of mass 30 kg runs at a speed of 5 m/sec tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglect friction and find the angular velocity of the merry-go-round and child

(a) 0.2 rad/sec (b) 0.1 rad/sec (c) 0.4 rad/sec (d) 0.8 rad/sec Ans. c (74)

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