A spherical planet far out in space has a mass `M_(0)` and diameter `D_(0)`. A particle of mass m falling freely near the surface of this planet will experience an accelertion due to gravity which is equal to

Options

A. `(4GM_P)/(D_P^2)`
B. `(GM_P m)/(D_P^2)`
C. `(4GM_P m)/(D_P^2)`
D. none of these

Answer

A

Explanation

Gravitational force acting on particle of mass m is
` F =(GM_Pm)/((D_P//2)^2)`
Acceleration due to gravity experience by the particle is
` g = F/m = (GM_P)/((D_P//2)^2) =(4GM_P)/(D_P^2)`