The acceleration due to gravity near the surface of a planet of radius R and density d is

proportional to

1. $\frac{d}{R^2}$                            

2. $d{R}^2$

3. dR                             

4. $\frac{d}{r}$

The weight of a body at the centre of the earth is -

1. Zero                                         

2. Infinite

3. Same as on the surface of the earth

4. None of the above

If the radius of a planet is R and its density is $\mathrm{\rho }$, the escape velocity from its surface will

be

1. $V_e \propto pR$                         

2. $V_e \propto R\sqrt{\rho }$

3. $V_e\propto \frac{\sqrt{p}}{R}$                        

4. $V_e \propto \frac{1}{\sqrt{p}R}$

If the distance between two masses is doubled, the gravitational attraction between them:

1. Is doubled                               

2. Becomes four times

3. Is reduced to half                     

4. Is reduced to a quarter

If the earth stops rotating, the value of \(g\) at the equator will:
1. increase                            
2. remain same   
3. decrease
4. none of the above

If acceleration due to gravity on the surface of a planet is two times that on surface of

earth and its radius is double that of earth. Then escape velocity from the surface of that

planet in comparison to earth will be -

1. 2v_e                            

2. 3v_e

3. 4v_e                             

4. None of these

A body weight W newton at the surface of the earth. Its weight at a height equal to half

the radius of the earth will be

1. $\frac{w}{2}$                    

2. $2\frac{w}{3}$

3. $4\frac{w}{9}$                 

4. $\frac{8w}{27}$

The escape velocity of a rocket launched from the surface of the earth

1. Does not depend on the mass of the rocket

2. Does not depend on the mass of the earth

3. Depends on the mass of the planet towards which it is moving

4. None of the above

Which of the following is the evidence to show that there must be a force acting on earth

and directed towards the sun?

1. Deviation of the falling bodies towards east

2. Revolution of the earth around the sun

3. Phenomenon of day and night

4. The apparent motion of the sun around the earth

A mass of  $6\times {10}^{24} kg$ is to be compressed in a sphere in such a way that the escape

velocity from the sphere is $3\times {10}^{8 }m/s$. Radius of the sphere should be 

$\left(G=6.67\times {10}^{-11} N-m^2/k{g}^2\right)$

1. 9 km                     

2. 9 m

3. 9 cm                     

4. 9 mm