Question

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 1

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.