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A point mass M is placed at a distance a from the surface of a thin spherical shell that has the same mass M and radius a (so the point mass is at distance 2a from the shell's centre). Which statement is correct regarding the gravitational field and potential due to the shell?

1. Both the gravitational field and the potential are zero at the centre of the shell.
2. The gravitational field is zero not only inside the shell but also at a point outside it.
3. Inside the shell, only the gravitational field is zero (the potential is not).
4. Neither the gravitational field nor the gravitational potential is zero inside the shell.

Correct answer: Inside the shell, only the gravitational field is zero (the potential is not).

Solution

For a thin uniform spherical shell, the gravitational field at every interior point (including the centre) is zero, but the potential inside is constant and equals -G*M/a, which is not zero. So inside the shell the field is zero while the potential is non-zero.

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