A homogeneous spherical heavenly body has a uniform and very narrow frictionless duct along its diameter. Let mass of the body be `M` and diameter be `D`. A point mass `m` moves smoothly inside the duct. Force exerted on this mass when it is at a distance `s` from the centre of the body is (numerically)

Options

A. `(GMm)/(s^(2))`
B. `(piGMm)/((D//2)^(3))s`
C. `(8GMms)/(D^(3))`
D. `(GMm)/((R-s)^(2))`

Answer

C

Explanation

`M/(4/3pi(D/2)^(3))=(M_(s))/(4/3piS^(3)), F=-(GmM_(S))/(S^(2))`