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A spherical shell of mass m and radius R has a point mass m placed at an external point B. Point C is at the surface of the shell (on the side closer to B) and point D is at the surface on the opposite side from B. The distance from the shell's centre to B is 2R. Which of the following statements is/are correct?
- Gravitational potential energy of the system is -Gm²/(2R).
- Gravitational field at point C (surface on the side of B) is zero.
- Gravitational potential difference between point D and C is V_D - V_C = 4Gm/(15R).
- Gravitational potential due to the spherical shell at points C and D are equal.
Correct answer: Gravitational potential due to the spherical shell at points C and D are equal.
Solution
A uniform spherical shell produces the same gravitational potential (-Gm/R) at every point on its surface (inside is also -Gm/R). Hence the shell's own potential at C equals that at D. The other options involve incorrect numerical values that can be shown to not hold for standard geometry.
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