A solid sphere of mass M and radius R has a spherical cavity of radius R/2 such that the centre of cavity is at a distance R/2 from the centre of the sphere. A point mass `m` is placed inside the cavity at a distance R/4 from the centre of sphere. The gravitational force on mass `m` is

Options

A. `(11GMm)/(R^(2))`
B. `(14 GMm)/(R^(2))`
C. `(GMm)/(2R^(2))`
D. `(GMm)/(R^(2))`

Answer

C

Explanation

Field strength is uniform inside the cavity. Let us find at its centre
`E_(T)=E_(R)+E_(C)` (T = Total, R = Remaining, C = Cavity)
`:. E_(R)=E_(T)-E_(C)`
`=(GM)/(R^(3))(R)/(2)-0=(GM)/(2R^(2))`
`:. F=mF_(R)=(GMm)/(2R^(2))`.