1. The mass of the earth is \[6.00\times 10^{24}kg\] and that of the moon is \[7.40\times 10^{22}kg\] . The constant of gravitation \[G=6.67\times 10^{-11}N-m^{2}\diagup kg^{2}\] . The
potential energy of the system is \[-7.79\times 10^{28}\] joules. The mean distance between the earth and moon is

a) \[3.80\times 10^{8}metres\]

b) \[3.37\times 10^{6}metres\]

c) \[7.60\times 10^{4}metres\]

d) \[1.90\times 10^{2}metres\]

Explanation:

2. The change in potential energy, when a body of mass m is raised to a height nR from the earth's surface is (R = Radius of earth)

a) \[mgR \frac{n}{n-1}\]

b) nmgR

c) \[mgR \frac{n^{2}}{n^{2}+1}\]

d) \[mgR \frac{n}{n+1}\]

Explanation:

3. The masses and radii of the earth and moon are \[M_{1}, R_{1}\] and \[M_{2}, R_{2}\] respectively. Their centres are
distance d apart. The minimum velocity with which a particle of mass m should be projected from a point midway between their centres so
that it escapes to infinity is

a) \[2\sqrt{\frac{G}{d}\left(M_{1}+M_{2}\right)}\]

b) \[2\sqrt{\frac{2G}{d}\left(M_{1}+M_{2}\right)}\]

c) \[2\sqrt{\frac{Gm}{d}\left(M_{1}+M_{2}\right)}\]

d) \[2\sqrt{\frac{Gm\left(M_{1}+M_{2}\right)}{d\left(R_{1}+R_{2}\right)}}\]

Explanation:

4. If mass of earth is M, radius is R and gravitational constant is G, then work done to take 1 kg mass from earth surface to infinity will be

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

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

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

d) \[\frac{Gm}{2R}\]

Explanation: Potential energy of the 1 kg mass which is placed at the earth surface = \[\frac{-GM}{R}\]

its potential energy at infinite = 0

Work done = change in potential energy = \[\frac{GM}{R}\]

5.A rocket is launched with velocity 10 km/s. If radius of earth is R, then maximum height attained by it will be

a) 2R

b) 3R

c) 4R

d) 5R

Explanation: 4R

6. There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of
gravitational field will be zero

a)\[\frac{1}{9}m\]

b) \[\frac{1}{10}m\]

c) \[\frac{1}{11}m\]

d) \[\frac{10}{11}m\]

Explanation:

7. What is the intensity of gravitational field of the centre of a spherical shell

a) \[Gm\diagup r^{2}\]

b) g

c) Zero

d) none of these

Explanation: Zero

8. The gravitational potential energy of a body of mass ‘m’ at the earth’s surface \[-mgR_{e}\] . Its gravitational potential energy at a height R_{e} from the earth’s surface will be (Here R_{e} is the radius of the earth)

a) \[-2mgR_{e}\]

b) \[2mgR_{e}\]

c) \[\frac{1}{2}mgR_{e}\]

d) \[-\frac{1}{2}mgR_{e}\]

Explanation:

9. Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the Planet is

a) – 5000 J

b) – 1000 J

c) – 2400 J

d) 5000 J

Explanation:

10. A body of mass m is placed on the earth’s surface. It is taken from the earth’s surface to a height \[h=3R\] . The change in gravitational potential energy of the body is

a) \[\frac{2}{3}mgR\]

b) \[\frac{3}{4}mgR\]

c) \[\frac{mgR}{2}\]

d) \[\frac{mgR}{4}\]

Explanation: