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)$g\left(1-\frac{h}{R}\right)$ 

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

(a)$\sqrt{2}$ times                    (b) 2 times

(c) 3 times                       (d) 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. $\frac{d}{r}$

The weight of a body at the centre of the earth is -

1. Zero                                         

2. Infinite

3. Same as on the surface of the earth

4. None of the above

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

be

1. $V_e \propto pR$                         

2. $V_e \propto R\sqrt{\rho }$

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

4. $V_e \propto \frac{1}{\sqrt{p}R}$