Question

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

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

Answer 1

Answer: (C)

For earth, $g=\frac{GM}{R^{2}}=\frac{4}{3}\pi RρG$
For the planet, $g_{1}=\frac{GM_{1}}{R_{1}^{2}}=\frac{4}{3} \, \pi R_{1}ρG$
$\frac{g}{g_{1}}=\frac{R}{R_{1}}=\frac{6400}{320}=20$
Let $h$ and $h_{1}$ be the distance up to which the man can jump on the surface of the earth and planet, then
$mgh=mg_{1}h_{1}$
$\therefore \, h_{1}=\frac{g}{g_{1}} \, h=20\times 5=100 \, m$