An isolated solid sphere of radius 
may be assumed to have its mass 
concentrated at its centre. The magnitude of the gravitational potential at the surface of the sphere is 
. On the figure below, show the variation of the gravitational potential with distance 
from the centre of the sphere for values of from 
to 
.
The sphere in (a) is a planet with radius of 
and mass of 
. The planet has no atmosphere. A rock of mass 
moves directly towards the planet. Its distance from the centre of the planet changes from 
to 
. Calculate the change in gravitational potential energy of the rock.
.
