A small mass m is transferred from the centre of a hollow sphere of mass M to infinity. Find work done in the process. Compare this with the situation if instead of a hollow sphere, a solid sphere of same mass were there.

A small mass m is transferred from the centre of a hollow sphere of ma

1.	A small mass m is transferred from the centre of a hollow sphere of mass M to infinity. Find work done in the process. Compare this with the situation if instead of a hollow sphere, a solid sphere of same mass were there.
Answer» Solution :We know at infinity gravitional potential is taken ZERO. Thus if `V_(C )` be the GRAVITATIONAL potential at centre of holow sphere then external work required the procedd is `W = m(0-V_(C ))` or `= m(0-((GM)/(R )))=(GMm)/(R )` Here `V_(C )= -(GM)/(R )`, the potential at the centre of a hollow sphere of mass M and radius R. If a so solid sphere is here, we have at its centre `V_(C )= - (3)/(2)(GM)/(R )` Thus work required will be `W = m[0-(-(3)/(2)(GM)/(R ))]=(3)/(2)(GMm)/(R )` We can SEE in second case more work is required for the process.