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

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

We know $g=\frac{GM}{R^2}=\frac{GM}{{\left(\frac{D}{2}\right)}^2}=\frac{4GM}{D^2}$

If mass of the planet = $M_0$ and diameter of the planet = $D_0$. Then $g=\frac{4G{M}_0}{D_0^2}$