Q. 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
A) $4GM_{P}/D_{P}^{2}$
B) $GM_{P}m/D_{P}^{2}$
C) $GM_{P}/D_{P}^{2}$
D) $4GM_{P}m/D_{P}^{2}$
Explanation
(a) Gravitational attraction force on particle $B$
$F_{g} = \frac{GM_{P}m}{\left( D_{P}/2 \right)^{2}}$
Acceleration of particle due to gravity $a = \frac{F_{g}}{m} = \frac{4GM_{P}}{D_{P}^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.