Question

$\begin{array}{c}\text{If the ratio of the masses of two planets is}8:3\text{and the ratio of their diameters is}2:3\text{, then}\\ \text{what will be the ratio of their acceleration due to gravity?}\end{array}$

Answer 1

Given,

Raito of mass,$\frac{M^{\prime \prime }}{M^{\prime }}=\frac{8}{3}$

Radio of Diameter or radius, $\frac{R^{\prime \prime }}{R^{\prime }}=\frac{2}{3}$

Acceleration of gravity,

$g=\frac{GM}{R^2}$

Ratio of gravity, $\frac{g^{\prime \prime }}{g^{\prime }}=\frac{M^{\prime \prime }}{M^{\prime }}{\left(\frac{R^{\prime }}{R^{\prime \prime }}\right)}^2=\frac{8}{3}\times {\left(\frac{3}{2}\right)}^2=6$

Hence, ratio of acceleration of gravity is $6$