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. $\frac{R}{8}$

The escape velocity from the surface of the earth is ${\mathrm{v}}_{\mathrm{e}}$. The escape velocity from the surface of a planet whose mass and radius are 3 times those of the earth will be:

1. ${\mathrm{v}}_{\mathrm{e}}$                                                             

2. 3${\mathrm{v}}_{\mathrm{e}}$

3. 9${\mathrm{v}}_{\mathrm{e}}$                                                           

4. 27${\mathrm{v}}_{\mathrm{e}}$

1. $About 9.8\times {10}^{6}J$                       
2. $About 6.4\times {10}^{8}J$
3. $About 3.1\times {10}^{10}J$                     
4. $About 27.4\times {10}^{12}J$

Two planets have the same average density but their radii are $R_1$  and $R_2$. If acceleration due to gravity on these planets be $g_1$ and $g_2$ respectively, then

1.  $\frac{g_1}{g_2}$= $\frac{R_1}{R_2}$                   

2. $\frac{g_1}{g_2}$=$\frac{R_2}{R_1}$

3.  $\frac{g_1}{g_2}$= $\frac{{R_1}^2}{{R_2}^2}$                  

4. $\frac{g_1}{g_2}$= $\frac{{R_1}^3}{{R_2}^3}$

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$R_{\epsilon }$

If the density of the earth is increased \(4\) times and its radius becomes half of what it is, our weight will be:
1. four times the present value
2. doubled
3. the same
4. Halved

The escape velocity on earth is 11.2 km/s. On another planet having twice radius and 8 times mass of the earth, the escape velocity will be

1. 3.7 km/s                                                  2. 11.2 km/s

3. 22.4 km/s                                                4. 43.2 km/s

When a body is taken from the equator to the poles, its weight 
1.   Remains constant           

2.  Increases

3.  Decreases                    

4.  Increases at N-pole and decreases at S-pole

The escape velocity of a body on the surface of the earth is 11.2 km/s. If the earth's mass increases to twice its present value and the radius of the earth becomes half, the escape velocity would become

1. 5.6 km/s                                            

2. 11.2 km/s (remain unchanged)

3. 22.4 km/s                                           

4. 44.8 km/s