Consider a solid sphere of density `rho` and radius `4R`. Centre of the sphere is at origin. Two spherical cavities centred at `(2R,0)` and `(-2R,0)` are created in sphere. Radii of both cavities is `R`. In left cavity material of density `2rho` is filled while second cavity is kept empty. What is gravitational field at origin.

Options

A. `(4GrhopiR)/3`
B. `(3GrhopiR)/2`
C. `(GrhopiR)/3`
D. `(2GrhopiR)/3`

Answer

D

Explanation

Above distribution canbe represented as shown in figure
Gravitation field due to sphere of radius `R` at a distance `2R`.
`E_(g)=(Grho 4/3piR^(3))/(4R^(2))=(GrhopiR)/3`
So net field at centre will be`2F_(g)=(2GrhopiR)/3`