Question

Escape velocity of a body on a planet is $100m{s}^{-1}$. What is the gravitational potential energy of the body at the surface, if the mass of the body is $1kg$?

• A. $-5000J$
• B. $-1000J$
• C. $-2400J$
• D. $5000J$

Answer 1

The correct option is A

$-5000J$

Given, escape velocity, $v_e=100m{s}^{-1}$, mass of the body, $m=1kg$
We know universal gravitational constant, $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$.
Let $M$ be the mass of the planet and $R$ be the radius of the planet and $U$ be the gravitational potential energy.
We know, $v_e=\sqrt{\frac{2GM}{R}}=100$
$\Rightarrow 10000=\frac{2GM}{R}\Rightarrow \frac{GM}{R}=5000$
Potential energy, $U=-\frac{GMm}{R}=5000\times 1=-5000J$