If R is the radius of the earth and g the acceleration due to gravity on the earth's surface,

the mean density of the earth is:

1. $4\pi G/3gR$                                 

2. $3\pi R/4gG$

3. $3g/4\pi RG$                               

4.$\pi RG/12G$        

A planet has twice the radius but the mean density is $\frac{1}{4}th$ as compared to earth. What is the ratio of escape velocity from earth to that from the planet ?

1. 3:1                                                                 

2. 1:2

3. 1:1                                                                 

4. 2:1

A body weighs 500 N on the surface of the earth. How much would it weigh halfway

below the surface of the earth?

1. 125 N                               

2.  250 N

3. 500 N                               

4.  1000 N

Who among the following gave first the experimental value of G?

1. Cavendish                               

2. Copernicus

3. Brook Taylor                           

4. None of these

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 weight of an object in the coal mine, sea level, at the top of the mountain are  $W_1$,

$W_2$ and $W_3$   respectively, then

1.  $W_1\le W_2\ge W_3$                      

2.  $W_1=W_2=W_3$

3.  $W_1\le W_2\le W_3$                     

4.  $W_1\ge W_2\ge W_3$      

The value of escape velocity on a certain planet is 2 km/s. Then the value of orbital speed

for a satellite orbiting close to its surface is:

1. 12km/s                                                                 

2. 1km/s

3. $\sqrt{2 } km/s$                                                             

4. $2\sqrt{2} km/s$

Four particles each of mass M, are located at the vertices of a square with side L. The

gravitational potential due to this at the centre of the square is

1. $-\sqrt{32}\frac{GM}{L}$                                   

2. $-\sqrt{64}\frac{GM}{L^2}$

3. zero                                             

4. $\sqrt{32}\frac{GM}{L}$

The mass of the moon is $7.34\times {10}^{22}kg$ and the radius is $1.74\times {10}^{6}m$. The value of

gravitation field will be

1. $1.45 N/kg$                               

2. $1.55 N/kg$

3. $1.75 N/kg$                               

4.  $1.62 N/kg$

The centripetal force acting on a satellite orbiting round the earth and the gravitational

force of earth acting on the satellite both equal F. The net force on the satellite is

1. Zero                                  

2. F

3. $F\sqrt{2}$                                 

4. 2 F