A spherical planet has a mass $M_p$ and diameter $D_p$. A particle of mass $m$ falling freely near the…

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
  1. $4 G M_p / D_p^2$
  2. $G M_p m / D_p^2$
  3. $G M_p m / D_p^2$
  4. $4 G M_p m / D_p^2$

Solution

Force,
$F=\frac{G M_e m}{R^2}$
Here, $F=\frac{G M_P m}{\left(D_P / 2\right)^2}$
$\begin{aligned}
& F=\frac{4 G M_P m}{D_P^2} \\
& F=m a
\end{aligned}$
Acceleration due to gravity
$a=\frac{F}{m}=\frac{4 G M_P}{D_P^2}$ .

Asked in: NEET 2012 (Screening)

Practice more Gravitation questions on Aicharya