Gravitation: Field Inside Solid Sphere MCQ

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Field Inside Solid SphereHardQuestion 30720

Question

Inside a uniform solid sphere of density ρ, radius R, the gravitational field at distance r from centre (r < R) is:

A
GM/r²
B
−4πGρr/3
C
4πGρr/3 (directed inward)
Correct
D
Zero

Correct answer

4πGρr/3 (directed inward)

Explanation

Only the mass within radius r contributes: M' = (4/3)πr³ρ. g = GM'/r² = G(4πr³ρ/3)/r² = 4πGρr/3. It increases linearly with r inside the sphere (directed toward centre).

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