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

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. $g\left(1-\frac{h}{R}\right)$