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

Answer

B

Explanation

To calculate the force of attraction on the point mass m we should calculate the force due to the solid spere and substract from this force which the mass o fhte hollow sphere would have exerted on m
`F=(GmM)/(x^(2))-(GmM)/(y^(2)) [therefore =R//4x+y=R//2]`

`M=(4/3)piR^(3)P`
and `M=4/3 pi (R)/(2)^(3)p=(M)/(8)`
`=(14GmM)/(R^(2))`