Suppose a vertical tunnel is dug along the diameter of earth , which is assumed to be a sphere of uniform mass density `rho`. If a body of mass `m` is thrown in this tunnel, its acceleration at a distance `y` from the centre is given by

Options

A. `(4pi)/(3) G rhoym`
B. `(3)/(4)pi rho y`
C. `(4)/(3) pi rho y`
D. `(4)/(3)pi G rho y`

Answer

D

Explanation

`a=g'=g(1-(h)/(R))=g((R-h)/(R))=(g)/(R).y" "(because (R-h)/(R)=y)`
`=(((GM)/(R^(2))))/(R).y=(G)/(R^(3))((4)/(3)piR^(3)rho).y=(4)/(3)pi rhoGy`.