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. $\frac{G{M}_p}{D_p^2}$
• B. $\frac{4G{M}_{p}m}{D_p^2}$
• C. $\frac{4G{M}_p}{D_p^2}$
• D. $\frac{G{M}_{p}m}{D_p^2}$

Answer 1

The correct option is C $\frac{4G{M}_p}{D_p^2}$

As we know that acceleration due to gravity, near surface is given by

$g=\frac{GM}{R^2}$

Here, $M=M_p;R=R_p$

So, acceleration due to gravity due given planet will be

$g_p=\frac{G{M}_p}{R_p^2}$

Here, $D_p=2R_p$

$\Rightarrow g_p=\frac{4G{M}_p}{D_p^2}$

Therefore, option $\left(c\right)$ is correct.

Why the question: To make students understand the quantities on which the acceleration due to gravity depends. Key Concept: Acceleration due to gravity on the surface of a planet is given by $g=GM/R^2$