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. `(mg)/4`

Answer

B

Explanation

`E_(1)=(rhoR)/(6epsilon_(0)),E_(c)=(-rho(R//2)^(3))/(3epsilon_(0)R^(2))`
`E_(net)=E_(1)+E_(c), rho=M/(4/3piR^(3)), epsilon_(0)=1/(4piG)`