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

Answer

B

Explanation

Force, `F=(GM_(E)m)/(R^(2))`
Here, `F=(GM_(p)m)/((D_(p)//2)^(2))=(4GM_(p)m)/(D_(p)^(2))`
we know `F=ma`
Acceleration due to gravity `a=F/m=(4GM_(p))/(D_(p)^(2))`