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 acceleration due to gravity which is equal to:

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

Answer 1

Answer: (C)

$\frac{4G{M}_0}{{\left(D_0\right)}^2}$

mass of the planet is $M_0$

diameter is $D_0$

radius $R=\frac{D_0}{2}$

$g=\frac{G{M}_0}{R^2}$

$g=\frac{G{M}_0}{(\frac{D_0}{2}{)}^2}$

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