CBSE Class 10 Physics Gravitation MCQs Set 07

Answer: (b) zero

Explanation:
1. For a point below the surface, \( g' = g(1 - d/R) \).
2. At the centre d = R, so g' = 0.

Teacher's Note:
1. The pull of the surrounding mass cancels out at the centre.

Answer: (a) It is a short-range force

Explanation:
1. Gravitation is a long-range force, effective over very large distances.
2. The other three statements are correct.

Teacher's Note:
1. Long range is one of its characteristic features.

Answer: (c) 24 hours

Explanation:
1. It must revolve in the same period as the earth rotates, so it appears fixed above one point.
2. The period is 24 hours.

Teacher's Note:
1. It orbits in the equatorial plane in the same direction as the earth's rotation.

Answer: (d) 6 kg

Explanation:
1. g on the planet = 15 m/s\( ^2 \).
2. m = W/g = 90/15 = 6 kg.

Teacher's Note:
1. Mass is the same anywhere.

Answer: (c) vector quantity measured in newton

Explanation:
1. Weight is the gravitational force on a body, directed towards the centre of the earth.
2. Force is a vector measured in newton.

Teacher's Note:
1. Mass is the scalar measured in kilogram.

Answer: (c) equally on both bodies, in opposite directions

Explanation:
1. Gravitational forces form an action-reaction pair (third law).
2. They are equal in magnitude and opposite in direction, each acting on a different body.

Teacher's Note:
1. Gravity is a non-contact force that acts at a distance.

Answer: (c) \( 6.67\times10^{-11} \) N

Explanation:
1. \( F = G \times 1 \times 1 / 1^2 = G \).
2. = \( 6.67\times10^{-11} \) N.

Teacher's Note:
1. This is the definition of G.

Answer: (d) \( 2.8\times10^{-7} \) N

Explanation:
1. \( F = Gm_1m_2/r^2 = 6.67\times10^{-11} \times 60 \times 70 / 1^2 \).
2. = \( 6.67\times10^{-11} \times 4200 = 2.8\times10^{-7} \) N.

Teacher's Note:
1. The force between ordinary objects is extremely small.
2. That is why we do not feel attraction to nearby objects.

Answer: (c) 3 : 1

Explanation:
1. \( v_A / v_P = r_P / r_A = 1/3 \).
2. So \( v_P : v_A = 3 : 1 \).

Teacher's Note:
1. At the extreme points the speed varies inversely with the distance.

Answer: (d) 8 years

Explanation:
1. \( T^2 \propto R^3 \), so \( T = 1 \times 4^{3/2} \) years.
2. \( 4^{1.5} = 8 \) years.

Teacher's Note:
1. Use the earth's period of 1 year as the reference.

Answer: (c) g/2

Explanation:
1. \( g \propto M/R^2 \).
2. Factor = 2 / 2^2 = 1/2, so the acceleration is g/2.

Teacher's Note:
1. Both changes act together: mass raises g, radius lowers it more.

Answer: (c) 35800 km

Explanation:
1. A period of 24 hours fixes the orbital radius.
2. The height above the surface is about 35800 km.

Teacher's Note:
1. Communication satellites use this orbit.

Answer: (d) is independent of m

Explanation:
1. \( v_e = \sqrt{2GM/R} \) contains only the mass and radius of the earth.
2. A spacecraft and a molecule have the same escape speed.

Teacher's Note:
1. Escape speed also does not depend on the direction of projection.

Answer: (b) zero

Explanation:
1. At the centre g = 0, so W = mg = 0.

Teacher's Note:
1. Mass is unchanged, but weight vanishes.

Answer: (a) the same

Explanation:
1. Mass is the amount of matter and does not change with location.

Teacher's Note:
1. Only weight depends on the value of g.

Answer: (d) 10 kg

Explanation:
1. W = mg, so m = 98 / 9.8 = 10 kg.

Teacher's Note:
1. Weight is in newton, mass in kilogram.

Answer: (d) \( \sqrt{2} \)

Explanation:
1. \( v_e = \sqrt{2gR} \) and \( v_o = \sqrt{gR} \).
2. Ratio = \( \sqrt{2} \).

Teacher's Note:
1. 11.2 / 7.9 = 1.41.

Answer: (a) cube of the semi-major axis of its orbit

Explanation:
1. Kepler's third law: \( T^2 \propto R^3 \), where R is the semi-major axis.

Teacher's Note:
1. The ratio \( T^2/R^3 \) is the same for all planets of the sun.

Answer: (d) one-fourth

Explanation:
1. \( F \propto 1/r^2 \).
2. With r doubled the force becomes \( 1/2^2 = 1/4 \) of the original.

Teacher's Note:
1. Inverse-square law: double the distance, quarter the force.

Answer: (a) \( 6.67\times10^{-11} \) N m\( ^2 \) kg\( ^{-2} \)

Explanation:
1. The experimentally measured value is \( 6.67\times10^{-11} \) N m\( ^2 \) kg\( ^{-2} \).
2. It is very small, which is why gravity is noticeable only for huge masses.

Teacher's Note:
1. Do not confuse G with g = 9.8 m/s\( ^2 \).

Answer: (b) 9 times

Explanation:
1. \( F \propto 1/r^2 \).
2. With r/3 the force becomes \( 3^2 = 9 \) times.

Teacher's Note:
1. Reducing the distance increases the force by the square of the factor.