If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth, the escape velocity for the body to escape out of the earth's gravitational field is:

1. gr                                       

2. $\sqrt{2gr}$

3. g/r                                       

4. r/g

The escape velocity of a particle of mass m varies as:

1. $m^2$                                   

2. m

3. $m^0$                                   

4. $m^{-1}$

The time period of a simple pendulum on a freely moving artificial satellite is

1. Zero                           

2. 2 sec

3.  3 sec                          

4.  Infinite

The escape velocity of an object from the earth depends upon the mass of the earth (M), its mean density, its radius (R) and the gravitational constant (G). Thus the formula for escape velocity is:

1. $v=R\sqrt{\frac{8\mathrm{\pi }}{3}Gp}$                                         

2. $v=M\sqrt{\frac{8\mathrm{\pi }}{3}GR}$

3. $v=\sqrt{2GMR}$                                             

4. $v=\sqrt{\frac{2GM}{R^2}}$

If radius of earth is R then the height h’ at which value of ‘g’ becomes one-fourth is 

1. $\frac{R}{4}$               

2. $\frac{3R}{4}$

3. R                 

4. $\frac{R}{8}$

Assume that the acceleration due to gravity on the surface of the moon is 0.2 times the acceleration due to gravity on the surface of the earth. If $R_E$ is the maximum range of a projectile on the earth’s surface, what is the maximum range on the surface of the moon for the same velocity of projection ?

1. 0.2$R_{\epsilon }$                     

2. 2$R_{\epsilon }$

3. 0.5$R_{\epsilon }$                     

4. 5$R_{\epsilon }$

How many times is escape velocity, of orbital velocity for a satellite revolving near earth?

1.$\sqrt{2}$ times                   
2. 2 times
3. 3 times                      
4. 4 times

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. $\frac{d}{r}$

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

be

1. $V_e<mspace\; width="1em"></mspace>\propto <mspace\; width="1em"></mspace>pR$                         

2. $V_e<mspace\; width="1em"></mspace>\propto <mspace\; width="1em"></mspace>R\sqrt{\rho }$

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

4. $V_e<mspace\; width="1em"></mspace>\propto \frac{1}{\sqrt{p}R}$