Question

Imagine a new planet having the same density as that of the earth but it is $3$ times bigger than the earth is size. If the acceleration due to gravity on the surface of the earth is g and that on the new planet is g', then what is the value of g'/g?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is A 3

let $g^{\prime }$ and $g$ is the acceleration due to gravity at the new planet and at Earth.

$\frac{g^{\prime }}{g}=\frac{\frac{G{M}^{\prime }}{R^{\prime 2}}}{\frac{GM}{R^2}}=\left(\frac{M^{\prime }}{M}\right)\times {\left(\frac{R}{R^{\prime }}\right)}^2=\left(\frac{V^{\prime }P}{VP}\right){\left(\frac{R}{R^{\prime }}\right)}^2[V^{\prime }=3V=>p.\frac{4}{3}\pi R^{\prime 3}=3p.\frac{4}{3}\pi R^3=>R^{\prime 3}=3R^3=>\frac{R^{\prime }}{R}=\left(3{)}^{\frac{1}{3}}\right]=\frac{\frac{4}{3}\pi R^{\prime 3}}{\frac{4}{3}\pi R^3}\times \frac{R^2}{R^{\prime 2}}=\frac{R^{\prime }}{R}=(3{)}^{\frac{1}{3}}$