Inside a uniform sphere of density `rho` there is a spherical cavity whose centre is at a distance `l` from the centre of the sphere. Find the strength of the gravitational field inside the cavity.

Options

A. `E=(-2)/3 piGrhol`
B. `E=(-4)/3piGrhol`
C. `E=(-4)/3pi^(2)Grhol`
D. `E=(-4)/3piGrho^(2)l^(2)`

Answer

B

Explanation

Let `E`= gravitational field at `x` due to the complete sphere `E_(1)`= field due to hole and `E_(2)`=field due to the remanning portion `E=E_(1)+E_(2) :. E_(2)=E-E_(1).....(i)`
`=(GM)/(x^(2))-(Gm)/((x-R/2)^(2))`
Here ,`M=4/3piR^(3)rho_(0)` and `m=4/3(R/2)^(3).rho_(0)`