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

(a) $About 9.8\times {10}^{6}J$                        (b) $About 6.4\times {10}^{8}J$

(c) $About 3.1\times {10}^{10}J$                      (d) $About 27.4\times {10}^{12}J$

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 ?

(a) 0.2$R_{\epsilon }$                     

(b) 2$R_{\epsilon }$

(c) 0.5$R_{\epsilon }$                     

(d) 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

(a) 3.7 km/s                                                  (b) 11.2 km/s

(c) 22.4 km/s                                                 (d) 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

Given mass of the moon is 1/81 of the mass of the earth and corresponding radius is 1/4 of the earth. If escape velocity on the earth surface is  11.2 km/s, the value of same on the surface of the moon is

(1)0.14 km/s                                                  (2)0.5 km/s

(3)2.5 km/s                                                    (4)5 km/s