1
###
The height at which the acceleration due to gravity becomes g/9

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

- (√2)R
- R/2
- R/√2
- 2R

2
###
Two bodies of masses m and 4m are placed at a distance r

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

- zero
- -4Gm/r
- -6Gm/r
- -9Gm/r

3
###
If suddenly the gravitational force of attraction between Earth

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

- move tangentially to the originally orbit in the same velocity
- continue to move in its orbit with same velocity
- become stationary in its orbit
- move towards the earth

4
###
The escape velocity for a body projected vertically upwards

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be

- 11/√2 m/s
- 11√2 km/s
- 22 km/s
- 11 km/s

5
###
The kinetic energy needed to project a body of mass

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

- mgR
- 2mgR
- mgR/4
- mgR/2

6
###
The escape velocity of a body depends upon mass as

The escape velocity of a body depends upon mass as

- m
^{0} - m
^{1} - m
^{2} - m
^{3}

7
###
The mass of a spaceship is 1000 kg. It is to be launched

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/s^{2} and 6400 km respectively. The required energy for this work will be

- 6.4 X 10
^{8}Joules - 6.4 X 10
^{9}Joules - 6.4 X 10
^{10}Joules - 6.4 X 10
^{11}Joules

8
###
Energy required to move a body of mass m from an orbit of radius 2R to 3R

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

- (GMm)/(3R
^{2}) - (GMm)/(6R)
- (GMm)/(8R)
- (GMm)/(12R
^{2})

9
###
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then:

- T
^{2}∝ r^{3} - T ∝ r
^{2} - T ∝ r
- T ∝ √r