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. $V_e \propto \frac{1}{\sqrt{p}R}$

If the distance between two masses is doubled, the gravitational attraction between them:

1. Is doubled                               

2. Becomes four times

3. Is reduced to half                     

4. Is reduced to a quarter

If the earth stops rotating, the value of \(g\) at the equator will:
1. increase                            
2. remain same   
3. decrease
4. none of the above

If acceleration due to gravity on the surface of a planet is two times that on surface of

earth and its radius is double that of earth. Then escape velocity from the surface of that

planet in comparison to earth will be -

1. 2v_e                            

2. 3v_e

3. 4v_e                             

4. None of these