A spherical planet has a mass `M_(p)` and diameter `D_(p)`. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity, equal to:

Options

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

Answer

A

Explanation

Gravitational attraction on the particle,
`F=G(M_(p)m)/((D_(p)//2)^(2))`
Acceleration due to gravity,
`g=(F)/(m)=(4GM_(p))/(D_(p)^(2))`