Question

How high a man be able to jump on the surface of a planet of radius $320km$ , but having density same as that of the earth if he jumps $5m$ on the surface of the earth? ( Radius of earth = $6400km$ )

• A. $60m$
• B. $80m$
• C. $100m$
• D. $120m$

Answer 1

Answer: (C)

For earth, $g=\frac{GM}{R^2}=\frac{4}{3}\pi R\rho G$
For the planet, $g_1=\frac{G{M}_1}{R_1^2}=\frac{4}{3}\pi R_1\rho G$
$\frac{g}{g_1}=\frac{R}{R_1}=\frac{6400}{320}=20$
Let $h$ and $h_1$ be the distance up to which the man can jump on the surface of the earth and planet, then
$mgh=m{g}_1{h}_1$
$\therefore h_1=\frac{g}{g_1}h=20\times 5=100m$