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

The angular velocity of rotation of star (of mass M and radius R) at which the matter start to escape from its equator will be

(1)$\sqrt{\frac{2G{M}^2}{R}}$                                             

(2)$\sqrt{\frac{2GM}{g}}$

(3)$\sqrt{\frac{2GM}{R^3}}$                                               

(4)$\sqrt{\frac{2GR}{M}}$

A body weighs 700 gm wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass $\frac{1}{7}$ of earth's mass and radius is half that of the earth ?

(1)  200 gm wt                         

(2)  400 gm wt     

(3)  50 gm wt

(4)  300 gm wt

What will be the acceleration due to gravity at height h if h >> R  where R is radius of earth and g is acceleration due to gravity on the surface of earth ?

(1) $\frac{g}{{\left(1+{\displaystyle \frac{h}{R}}\right)}^2}$               

(2) $g\left(1-\frac{2h}{R}\right)$

(3) $\frac{g}{{\left(1-{\displaystyle \frac{h}{R}}\right)}^2}$                 

(4)$g\left(1-\frac{h}{R}\right)$