Two identical hollow spheres of negligible thickness are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere):

1.  R

2.  $R^2$

3.  $R^4$

4.  $R^3$

A planet is revolving around a massive star in a circular orbit of radius R. If the gravitational force of attraction between the planet and the star is inversely proportional to ${\mathrm{R}}^3$, then the time period of revolution T is proportional to:

1. ${\mathrm{R}}^5$

2. ${\mathrm{R}}^3$

3. ${\mathrm{R}}^2$

4. R

When a planet revolves around the sun in an elliptical orbit, then which of the following remains constant?

A satellite of mass 1000 kg revolves in a circular orbit around the earth with a constant speed of 100 m/ s. The total mechanical energy of the satellite is:

The value of acceleration due to gravity at a height of 800 km from the surface of the earth (radius of the earth is 6400 km and value of acceleration due to gravity on the earth's surface is 981 cm/${\mathrm{s}}^2$) is:

A satellite of mass m revolving around the earth in a circular orbit of radius r has its angular momentum equal to L about the centre of the earth. The potential energy of the satellite is: 

If the speed of an artificial satellite revolving around the earth in a circular orbit be \(2 \over 3\) of the escape velocity from the surface of earth then its altitude above the surface of the earth is

If R is the radius of the orbit of a planet and T is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?

1.		2.
3.		4.

The figure shows a planet in an elliptical orbit around the sun (S). The ratio of the momentum of the planet at point A to that at point B is:

Three identical point masses, each of mass 1 kg lie at three points (0, 0), (0, 0.2 m), (0.2 m, 0). The net gravitational force on the mass at the origin is:
1. \(6.67\times 10^{-9}(\hat i +\hat j)~\text{N}\)
2. \(1.67\times 10^{-9}(\hat i +\hat j) ~\text{N}\)
3. \(1.67\times 10^{-9}(\hat i -\hat j) ~\text{N}\)
4. \(1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}\)