Question

Pick out the correct relation(s) between universal gravitational constant $\left(G\right)$ and acceleration due to gravity $\left(g\right)$
M = mass of earth,
R = radius of earth.

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

Answer 1

Answer: (A), (C)

The correct options are
A $g=\frac{GM}{R^2}$
C $G=\frac{g{R}^2}{M}$

As we know the gravitational force is written as:
$F=\frac{GMm}{R^2}$ -----eq $\left(1\right)$
From Newton's second law, $F=mg$, where $g$ is the acceleration due to gravity and therefore acceleration is written as $g=\frac{F}{m}$

so after substituting $g$ in eq $\left(1\right)$, we get
$g=\frac{GM}{R^2}$ or $G=\frac{g{R}^2}{M}$