1.A body of mass m kg. starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface [R-Radius of Earth, M-Mass of Earth, G-Gravitational Constant]

a) \[\frac{1}{2}\frac{GMm}{R}\]

b) \[\frac{1}{6}\frac{GMm}{R}\]

c) \[\frac{2}{3}\frac{GMm}{R}\]

d) \[\frac{1}{3}\frac{GMm}{R}\]

Explanation:

2. A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet.
The maximum height attained by the body is

a) R/3

b) R/2

c) R/4

d) R/5

Explanation:

3. Energy required to move a body of mass m from an orbit of radius 2R to 3R is

a) \[GMm\diagup 12R^{2}\]

b) \[GMm\diagup 3R^{2}\]

c) \[GMm\diagup 8R\]

d) \[GMm\diagup 6R\]

Explanation:

4.The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is

a) mgR/2

b) 2 mgR

c) mgR

d) mgR/4

Explanation:

5. Radius of orbit of satellite of earth is R. Its kinetic energy is proportional to

a) \[\frac{1}{R}\]

b) \[\frac{1}{\sqrt{R}}\]

c) R

d) \[\frac{1}{R^{3/2}}\]

Explanation:

6. In some region, the gravitational field is zero. The gravitational potential in this region

a) Must be variable

b) Must be constant

c) Cannot be zero

d) Must be zero

Explanation:

7. A particle falls towards earth from infinity. It’s velocity on reaching the earth would be

a) Infinity

b) \[\sqrt{2gR}\]

c) \[2\sqrt{gR}\]

d) Zero

Explanation:

8. Gas escapes from the surface of a planet because it acquires an escape velocity. The escape velocity will depend on which of the following factors :

I. Mass of the planet

II. Mass of the particle escaping

III. Temperature of the planet

IV. Radius of the planet

Select the correct answer from the codes given below :

a) I and II

b) II and IV

c) I and IV

d) I, III and IV

Explanation:

9. \[V_{e}\] and \[V_{p}\] denotes the escape velocity from the earth and another planet having twice the radius and the same mean density as the earth. Then

a) \[V_{e}=V_{p}\]

b) \[V_{e}=V_{p}\diagup 2\]

c) \[V_{e}= 2V_{p}\]

d) \[V_{e}=V_{p}\diagup 4\]

Explanation:

10.The escape velocity of a sphere of mass m from earth having mass M and radius R is given by

a) \[\sqrt{\frac{2GM}{R}}\]

b) 2\[\sqrt{\frac{GM}{R}}\]

c) \[\sqrt{\frac{2GMm}{R}}\]

d) \[\sqrt{\frac{GM}{R}}\]

Explanation: Escape velocity does not depend on the mass of the projectile