Question

The expression for acceleration due to gravity $\left(g\right)$ near the surface of a planet of mass $\left(M\right)$ and radius $\left(r\right)$ is:

G: Gravitational constant

• A. $g=\frac{GM}{r}$
• B. $g=\frac{GM}{r^2}$
• C. $g=\frac{GM}{r^3}$
• D. $g=\frac{G{M}^2}{r}$

Answer 1

The correct option is B $g=\frac{GM}{r^2}$

Gravitational force between a body of mass $m$ and planet of mass $M$ is given by:
$F=G\frac{Mm}{r^2}$
where:
$G:$ Gravitational constant
$r:$ Radius of the planet

By newton's second law, Force on the body is:
$F=mg$

Equating the above two equations, we get:
$mg=G\frac{Mm}{r^2}$
$g=G\frac{M}{r^2}$