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 solid sphere]

Options

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

Answer

B

Explanation

Mass of sphere `MpropR^(3)`. If mass of complete sphere is `M`,then the mass of cavity will be `M//8`.
Using the figure `F=`force due to whole sphere `-` force due to gravity.
`F=(GMm)/(R^(3))(R/2)-(G(m//8)m)/((R)^(2))`
`(GMm)/(R^(2)) (R^(2))/2-(G(M//8)m)/(R^(2))`
`(GMm)/(R^(2))[4/8-1/8]=3/8(GMm)/(R^(2))=3/8mg`