A solid sphere of constant density p has mass M and radius R. What is the gravitational potential difference between a point P which is at distance  from the central and its surface?

(i.e. V_p - V_surface)

Concept:

Gravitational potential due to solid sphere given as

At internal point, potential difference is at distance r is given as

r is the distance from the center of the point, R is the radius of the spehre. 

Calculation:

Ar surface, r = R 

 -- (1)

At distance r = R /2 from the center

 -- (2)

Potential difference is V (R/2) - V (R)

So, the correct option is 

Additional InformationThe potential difference outside the sphere is given as