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

Answer 1

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

The correct option is A.

Given,

Mass of the spherical planet is $M_p$

Diameter of the spherical planet is $D_p$

Mass of the particle is $m$

So,

As we know,

$g=\frac{G{M}_p}{R^2}$

$R=\frac{D_p}{2}$

so,

$g=\frac{G{M}_p}{(\frac{D_p}{2}{)}^2}$

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