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For a uniform solid sphere of radius $r$ and mass $m$, if the gravitational potential on the surface is assumed to be zero, find the potential at the center.

I can't seem to figure out a way to do this. The only thing I know is the formula for gravitational potential for points inside a solid sphere if potential at infinity is assumed to be zero. But that doesn't work here, does it?

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  • $\begingroup$ You mean gravitational potential energy at center? $\endgroup$
    – QuIcKmAtHs
    Jan 1, 2018 at 9:24
  • $\begingroup$ Yep. Though John Rennie’s answer cleared my doubts… $\endgroup$
    – Senthil Arihant
    Jan 2, 2018 at 3:31

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You can take the zero point of your potential energy to be anywhere you want. It isn't possible to measure the absolute value of the potential energy, only differences in potential energy, so we can add an arbitrary constant to the potential energy without changing anything observable.

So suppose you define your potential energy to be zero at infinity, then you have:

PE

If you want to make the PE at the surface zero just subtract $V_s$ from all the values. That makes the PE at infinity $-V_s$ and the PE at the centre $V_c-V_s$.

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