Question

Acceleration due to gravity $g$ near the surface of a planet of mass $M$ and radius $R$ is given by:
$G$ is the Universal constant.

• A. $g=\frac{GM}{R}$
• B. $g=\frac{GR}{M^2}$
• C. $g=\frac{G{M}^2}{R}$
• D. $g=\frac{GM}{R^2}$

Answer 1

The correct option is D $g=\frac{GM}{R^2}$

Let the mass of body be $m$.

According to universal law of gravitation:
$F=\frac{GMm}{R^2}$

From Newton's second laws of motion,
$F=mg$

From above two equations,
$mg=\frac{GMm}{R^2}$
$g=\frac{GM}{R^2}$