Question

Calculate the escape velocity on the surface of the moon, if the mass and radius of the moon are $7.34\times {10}^{22}kg$ and $1.74\times {10}^{6}m$ respectively.

• A. $4.7km{s}^{-1}$
• B. $3.37km{s}^{-1}$
• C. $2.37km{s}^{-1}$
• D. $2km{s}^{-1}$

Answer 1

The correct option is C

$2.37km{s}^{-1}$

Given: Gravitational constant $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$
Mass of moon, $M=7.34\times {10}^{22}kg$
Radius of the moon, $R=1.74\times {10}^{6}m$
We know, escape velocity, $v_{esc}$ = $\sqrt{\frac{2GM}{R}}$
$\therefore v_{esc}=\sqrt{\frac{2\times 6.67\times {10}^{-11}\times 7.34\times {10}^{22}}{1.74\times {10}^6}}=2.37km{s}^{-1}$