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Two concentric spherical shells have masses M and m and radii R and r respectively, with R > r. What is the gravitational potential at their common centre?

1. -G*M/R
2. -G*M/r
3. -G*(M/R - m/r)
4. -G*(M/R + m/r)

Correct answer: -G*(M/R + m/r)

Solution

At the centre, each shell contributes its surface potential (constant inside a shell). Outer shell (mass M, radius R): potential = -G*M/R. Inner shell (mass m, radius r): potential = -G*m/r. Potentials add as scalars: V = -G*M/R - G*m/r = -G*(M/R + m/r).

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