Question

A planet is having a mass twice to that of earth's mass and its radius as 4 times that of earth's radius. Determine the acceleration due to gravity at the surface of this planet. Acceleration due to gravity at earth's surface is $10{\text{ms}}^{-2}$.

Answer 1

Acceleration due to gravity:

It is the acceleration gained by a body due to the gravitational force of attraction exerted by the earth.

The acceleration due to gravity on the surface of the earth is expressed as $g=\frac{GM}{R^2}$

Here, G = gravitational constant($6.67\times {10}^{-11}{\text{Nm}}^2{\text{kg}}^{-2}$)

M= mass of earth

R = radius of the earth

Given data and calculations:

Mass of planet, $M_P=2M$

The radius of planet, $R_P=4R$

Acceleration due to gravity at the surface of this planet,

$\begin{array}{rcl}{g}_P& =& \frac{G{M}_P}{{R_P}^2}\\ & =& \frac{G\times 2M}{{\left(4R\right)}^2}\\ & =& \frac{2}{16}\frac{GM}{R^2}\\ & =& \frac{g}{8}\end{array}$

Acceleration is due to gravity at the earth's surface,$g=10{\text{ms}}^{-2}$.

Therefore,

$\begin{array}{rcl}{g}_P& =& \frac{g}{8}\\ & =& \frac{10}{8}\\ & =& 1.25{\text{ms}}^{-2}\end{array}$

Thus, acceleration due to gravity at the surface of this planet is $1.25{\text{ms}}^{-2}$