Question

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

• A. $\frac {4GM_p}{D_p^2} $
• B. $\frac {GM_pm}{D_p^2} $
• C. $\frac {GM_p}{D_p} $
• D. $\frac {4GM_pm}{D_p^2} $

Answer 1

Answer: (A)

Gravitational force acting on particle of mass $m$ is
$F=\frac{G M_{p} m}{\left(D_{p} / 2\right)^{2}}$
Acceleration due to gravity experience by the particle is
$g=\frac{F}{m}=\frac{G M_{p}}{\left(D_{p} / 2\right)^{2}}=\frac{4 G M_{p}}{D_{p}^{2}}$