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83. A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved

(a) Centre of the circle (b) On the circumference of the circle (c) Inside the circle (d) Outside the circle Ans. a (5)

81. A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by 1%. Its angular speed

(a) Will increase approximately by 1% (b) Will decrease approximately by 1% (c) Will decrease approximately by 0.67% (d) Will decrease approximately by 0.33% Ans. c (7)

A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity ω. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity

(a) ω(M-2m) /(M+2m) (b) ωM/M+2m) (c) ωM/M+m (d) ω(M+2m)/M Ans. b (39)

77. A uniform heavy disc is rotating at constant angular velocity ω about a vertical axis through its centre and perpendicular to the plane of the disc. Let L be its angular momentum. A lump of plasticine is dropped vertically on the disc and sticks to it. Which will be constant

(a) w (b) w and L both (c) L only (d) Neither w nor L Ans. c (45)

75. A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O

(a) mvL (b) mvl (c) mvr (d) Zero Ans. b (3)

The density of a newly discovered planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of the earth. If the radius of the earth is R, the radius of the planet would be

(a) 2R (b) 4R (c) 1/4 R …

74. A disc is rotating with an angular speed of ω. If a child sits on it, which of the following is conserved

(a) Kinetic energy (b) Potential energy (c) Linear momentum (d) Angular momentum Ans. d (11)

73. The motion of planets in the solar system is an example of the conservation of

(a) Mass (b) Linear momentum (c) Angular momentum (d) Energy Ans. c (7)

If both the mass and the radius of the earth decrease by 1%, the value of the acceleration due to gravity will

(a) Decrease by 1% (b) Increase by 1% (c) Increase by 2% (d) Remain unchanged Answer: b (8)

73. Weight of a body of mass m decreases by 1% when it is raised to height h above the earth’s surface. If the body is taken to a depth h in a mine, change in its weight is

(a) 2% decrease (b) 0.5% decrease (c) 1% increase (d) 0.5% increase Answer: b (6)

The depth at which the effective value of acceleration due to gravity is g/4 is

(a) R (b) 3R/4 (c) R/2 (d) R/4 Answer: b (4)

72. A thin rod of length L and mass M is bent at the middle point O at an angle of 60 degree as shown in figure. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

(a) ML2/6 (b) ML2/12 (c) ML2/24 (d) ML2/3 Ans. b (29)

71. The acceleration of a body due to the attraction of the earth (radius R) at a distance 2 R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

(a) g/9 (b) g/3 (c) g/4 …

Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth ( pe ) and moon ( pm ) is ( pe/pm ) = 5/3 then radius of moon Rm in terms of Re will be

(a) 5/18 Re (b) 1/6 Re (c) 3/18 Re (d) 1/2√3 Re Answer: …

71. The moment of inertia I of a solid sphere having fixed volume depends upon its volume V as

(a) I ∝ V (b) I ∝ V2/3 (c) I ∝ V5/3 (d) I ∝ V3/2 Ans. c (10)

70. Four solids are shown in cross section. The sections have equal heights and equal maximum widths. They have the same mass. The one which has the largest rotational inertia about a perpendicular through the centre of mass is

Ans. a (126)

A research satellite of mass 200 kg circles the earth in an orbit of average radius 3R/2 where R is the radius of the earth. Assuming the gravitational pull on a mass of 1 kg on the earth’s surface to be 10 N, the pull on the satellite will be

(a) 880 N (b) 889 N (c) 890 N (d) 892 N Answer: a (4)

If the value of ‘g’ acceleration due to gravity, at earth surface is 10 m/s2 , its value in m/s2 at the centre of the earth, which is assumed to be a sphere of radius ‘R’ metre and uniform mass density is

(a) 5 (b) 10/R (c) 10/2R (d) Zero Answer: d (13)

The acceleration due to gravity at pole and equator can be related as

(a) gp < ge (b) gp = ge = g (c) gp = ge < g (d) gp > ge Answer: d (12)

If the density of the earth is doubled keeping its radius constant then acceleration due to gravity will be (g=9.8 m/s2 )

(a) 19.6 m/s2 (b) 9.8 m/s2 (c) 4.9 m/s2 (d) 2.45 m/s2 Answer: a (9)

A body weight W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be

(a) W/2 (b) 2W/3 (c) 4W/9 (d) …

The acceleration due to gravity is g at a point distant r from the centre of earth of radius R. If r < R , then

(a) g ∝ r (b) g ∝ r2 (c) g ∝ r-1 (d) g ∝ r-2 Answer: a (11)

If density of earth increased 4 times and its radius become half of what it is, our weight will

(a) Be four times its present value (b) Be doubled (c) Remain same (d) Be halved Answer: b (3)

At what distance from the centre of the earth, the value of acceleration due to gravity g will be half that on the surface (R = radius of earth)

(a) 2 R (b) R (c) 1.414 R (d) 0.414 R Answer: d (4)

The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to

(a) d/R2 (b) dR2 (c) dR (d) d/R Answer: c (9)

What will be the acceleration due to gravity at height h if h >> R. Where R is radius of earth and g is acceleration due to gravity on the surface of earth

(a) g/(1 + h/R )2 (b) g ( 1 – 2h/R ) (c) g/( 1- h/R )2 (d) g ( …

Weight of a body is maximum at

(a) Moon (b) Poles of earth (c) Equator of earth (d) Centre of earth Answer: b (5)

A man can jump to a height of 1.5 m on a planet A. What is the height he may be able to jump on another planet whose density and radius are, respectively, one-quarter and one-third that of planet A

(a) 1.5 m (b) 15 m (c) 18 m (d) 28 m Answer: c (4)

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX’ is

(a) ρL3/8π2 (b) ρL3/16π2 (c) 5ρL3/16π2 (d) 3ρL3/8π2 Ans. d (8)

63. Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1 : 3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio

(a) 1 : 3 (b) 3 : 1 (c) 1 : 9 (d) 9 : 1 Ans. b (45)

The angular speed of earth, so that the object on equator may appear weightless (g = 10 m/s2 , is , radius of earth 6400 km)

(a) 1.25×10-3 rad/sec (b) 1.56 ×10-3 rad/sec (c) 1.25×10-1 rad/sec (d) 1.56 rad/sec Answer: a (4)

68. A thin wire of length l and mass M is bent in the form of a semi-circle. What is its moment of inertia about an axis passing through the ends of the wire

(a) ML2/2 (b) ML2/π2 (c) 2ML2/ π2 (d) 2ML2/2π2 Ans. d (3)

Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If Re is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection

(a) 0.2 Re (b) 2 Re (c) 0.5 Re (d) …

If the mass of earth is 80 times of that of a planet and diameter is double that of planet and ‘g’ on earth is 9.8 m/s2 , then the value of ‘g’ on that planet is

(a) 4.9 m/s2 (b) 0.98 m/s2 (c) 0.49 m/s2 (d) 49 m/s2 Answer: c (6)

R and r are the radii of the earth and moon respectively. pe and pm are the densities of earth and moon respectively. The ratio of the accelerations due to gravity on the surfaces of earth and moon is

(a) R/r pe/ pm (b) r/R pe/ pm (c) r/R pe/ pm (d) R/r pe/ pm Answer: a (6)

66. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

(a) 0.4 m from mass of 0.3 kg (b) 0.98 from mass of 0.3 kg (c) 0.70 m from mass of 0.7 kg (d) 0.98 m from mass of 0.7 kg Ans. b (7)

65. If solid sphere and solid cylinder of same radius and density rotate about their own axis, the moment of inertia will be greater for (L = R)

(a) Solid sphere (b) Solid cylinder (c) Both (d) Equal both Ans. a (45)

Assuming earth to be a sphere of a uniform density, what is the value of gravitational acceleration in a mine 100 km below the earth’s surface (Given R = 6400 km)

(a) 9.66 m/s2 (b) 7.64 m/s2 (c) 5.06m/s2 (d) 3.10 m/s2 Answer: a (5)

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on 60o latitude becomes zero is (Radius of earth = 6400 km. At the poles g=10 ms-2)

(a) 2.5 × 10-3 rad /s (b) 5.0 × 10-1 rad /s (c) 10 × 101 rad /s (d) 7.8 × 10-2 rad /s Answer: a (5)

62. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

(a) 1/2 MR2 (b) 1/4 MR2 (c) 1/8 MR2 (d) √2 MR2 Ans. a (6)

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