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. $GM_{0}/D_{0}^{2}$
• B. $4mGM_{0}/D_{0}^{2}$
• C. $4GM_{0}/D_{0}^{2}$
• D. $GmM_{0}/D_{0}^{2}$

Answer 1

Answer: (C)

$4GM_{0}/D_{0}^{2}$

Answer 2

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

If mass of the planet $= M_{0}$ and diameter of the planet $= D_{0}$. Then $g = \frac{4GM_{0}}{D_{0}^{2}}$.