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A hollow spherical shell is compressed so that its radius becomes half its original value. How does the gravitational potential at the centre of the shell change?

1. increases
2. decreases
3. remains the same
4. first increases during compression, then returns to the original value

Correct answer: decreases

Solution

The potential inside (including at the centre of) a uniform shell is constant and equal to -G*M/R. Halving R doubles the magnitude, making V more negative, i.e. it decreases (becomes more negative).

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