Four particles each of mass M, are located at the vertices of a square with side L. The

gravitational potential due to this at the centre of the square is

1. $-\sqrt{32}\frac{GM}{L}$                                   

2. $-\sqrt{64}\frac{GM}{L^2}$

3. zero                                             

4. $\sqrt{32}\frac{GM}{L}$

The gravitational field due to a mass distribution is $E=K/x^3$ in the x-direction. (K is a

constant). Taking the gravitational potential to be zero at infinity, its value at a distance x

is

1. K/x                    

2. K/2x

3. $K/x^2$                 

4. K/2$x^2$

At what height from the surface of earth the gravitation potential and the value of g are $-5.4\times {10}^{7}J$ $k{g}^{-2}$ and $6.0$ $m{s}^{-2}$ respectively? (Take, the radius of earth as 6400 km.)

(a) 1600 km             (b) 1400 km 

(c) 2000 km             (d) 2600 km

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m,  4m, 8m, respectively from the origin. The resulting gravitational potential due to this system at the origin will be

(a)-G

(b)-8/3G

(c)-4/3G

(d)-4G

A particle of mass M is situated at the centre of a spherical shell of mass M and radius a.The gravitational potential at a point situated at a/2 distance from the centre will be 

1. $-\frac{3GM}{a}$                                       2. $-\frac{2GM}{a}$

3. $-\frac{GM}{a}$                                         4. $-\frac{4GM}{a}$