Suppose a verticle tunnel is dug along the diametal of earth , which is assumed to be a sphere of unifrom mass density `rho`. If a body of mass `m` is throws in this tunal, its acceleration at a distance `y` from the centre is given by

Options

A. `(4 pi)/(3) G rho Ym`
B. `(3)/(4) pi rho Y`
C. `(4)/(3) pi rho Y`
D. `(4)/(3) pi Grho Y`

Answer

D

Explanation

` a = E = ((GM)/(R^(3)) Y` (as `a = E = (F)/(m))`
`= (G((4)/(3) pi R^(3) rho))/(R^(3)) y = (4)/(3) pi G rho y`