3 particles each of mass m are kept at vertices of an equilateral triangle of side L. The gravitational field at centre due to these particles is

1. zero                                                                       

2. $\frac{3GM}{L^2}$

3. $\frac{9GM}{L^2}$                                                                     

4. $\frac{12}{\sqrt{3}}\frac{GM}{L^2}$

The centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to \(F\). The net force on the satellite is:
1. zero
2. \(F\)
3. \(F\sqrt{2}\)
4. \(2F\)

Two sphere of mass m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

1. F                                        

2. $\frac{F}{3}$  

3. $\frac{F}{9}$                                      

4. 3 F

Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to:
1. \(R^2\)
2. \(R^{-2}\)
3. \(R^4\)
4. \(R^{-4}\)

An astronaut orbiting the earth in a circular orbit 120 km above the surface of the earth, gently drops a spoon out of the spaceship. The spoon will:

1. Fall vertically down to the earth

2. Move towards the moon

3. Will move along with space-ship

4. Will move in an irregular way then fall down

Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution T. If the gravitational force of attraction between planet and star is proportional to ${\mathrm{R}}^{\frac{-5}{2}}$, then ${\mathrm{T}}^2$ is proportional to:

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

2. ${\mathrm{R}}^{7/2_{}^{}}$

3. ${\mathrm{R}}^{5/2}$                           

4. ${\mathrm{R}}^{3/2}$

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

1. 1/3                           

2. 1/2

3. 1/4                           

4. 1/5

Two identical satellites are at R and 7R away from the earth surface, the wrong statement is (R = Radius of the earth)

1. Ratio of total energy will be 4

2. Ratio of kinetic energies will be 4

3. Ratio of potential energies will be 4

4. Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

A body of mass m is taken from earth's surface to the height h equal to the radius of the earth, the increase in potential energy will be:

1. mgR                                

2. $\frac{1}{2}$mgR

3. 2mgR                             

4. $\frac{1}{4}$ mgR