Figure shows a spherical cavity inside a lead sphere. The surface of the cavity passes through the centre of the sphere and touches the right side of the sphere. The mass of the sphere before hollowing was `M`. With what gravitational force does the hollowed out lead sphere attract a particle of mass `m` that lies at a distance `d` from the centre of the lead sphere on the straight line connecting the centres of the spheres and of the cavity.

Answer

A, B, D

Explanation

Radius of hollow sphere is `(R )/(2)`, so mass in this hollow
portion would had been, `(M)/(8)`.
Now, net force on `m` due to whole sphere = force due to remaining mass + force due to cavity mass.
`:.` Force due to remaining mass = force due to whole sphere - force due to cavity mass
`= (GMm)/(d^(2)) - (G Mm)/(8(d - R//2)^(2))`
`= (G Mm)/(d^(2)) [ 1- (1)/(8(1 -(R )/(2d))^(2))]`