Question

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 acceleration due to gravity which is equal to:

• A. $\frac{G{M}_0}{D_0^2}$
• B. $\frac{4mG{M}_0}{D_0^2}$
• C. $\frac{4G{M}_0}{D_0^2}$
• D. $\frac{Gm{M}_0}{D_0^2}$

Answer 1

The correct option is C $\frac{4G{M}_0}{D_0^2}$

$D_0$ is the diameter of planet

Gravitational force on the body$\left(F\right)=\frac{4Gm{M}_0}{D_0^2}$

By Newton's Second Law

$F=m{a}_g$

$\Rightarrow a_g=\frac{4Gm{M}_0}{m{D}_0^2}$

$\Rightarrow a_g=\frac{4G{M}_0}{D_0^2}$