A cavity of radius `R//2` is made inside a solid sphere of radius `R`. The centre of the cavity is located at a distance `R//2` from the centre of the sphere. The gravitational force on a particle of a mass `'m'` at a distance `R//2` from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity). [Here `g=GM//R^(2)`, where `M` is the mass of the solide sphere]

Options

A. `(mg)/(2)`
B. `(3mg)/(8)`
C. `(mg)/(16)`
D. None of these

Answer

B

Explanation

`F_("net")=` force due for sphere +force dur for cavity
`=(GMm)/(R^(3))((R)/(2))+0implies(GMm)/(2R^(2))=(mg)/(2)`