Question

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of earth's radius $R$ will be

• A. $\frac{R}{4}$
• B. $\frac{R}{2}$
• C. $\frac{R}{3}$
• D. $\frac{R}{8}$

Answer 1

Answer: (B)

$\frac{R}{2}$

$g=\frac{GM}{R^2}=\frac{G\left(\frac{4}{3}\pi R^3\rho \right)}{R^2}$
or $g\propto \rho R$
$g_1=g_2$
$\therefore {\rho }_1{R}_1={\rho }_2{R}_2$
or $R_2=\frac{{\rho }_1}{{\rho }_2}\cdot R_1=\left(\frac{1}{2}\right)R=\frac{R}{2}$