Question

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

Answer 1

$q^{\prime }=\frac{GM}{R^2}$

$=\frac{G\times 2me}{{\left(4ve\right)}^2}$

$=\frac{1}{8}\frac{Gme}{v{e}^2}$

$=\frac{g}{8}$

To find $4$ times the acceleration due to gravity $=4\times \frac{1}{8}g=\frac{g}{2}=\frac{10}{2}$

$=5m/s^2$

Hence, the answer is $5m/s^2.$