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. `4 GM_(p)//D_(p)^(2)`
B. `GM_(p)m//D_(p)^(2)`
C. `GM_(p)m//D_(p)^(2)`
D. `4GM_(p)m//D_(p)^(2)`

Answer

A

Explanation

Force, `F=(GM_(e)m)/(R^(2))`
Here, `F=(GM_(P)m)/((D_(P)//2)^(2))rArrF=(4GM_(P))/(D_(P)^(2))rArrF=ma`
Acceleration due to gravity, `a=(F)/(m)=(4GM_(P))/(D_(P)^(2))`.