Question

The escape velocity of a body from earth is about $11.2km/s$. Assuming the mass and radius of the earth to be about $81$ and $4$ times the mass and radius of the moon, the escape velocity in $km/s$ from the surface of the moon will be

• A. 0.54
• B. 2.48
• C. 11
• D. 49.5

Answer 1

Answer: (B)

$V_{\text{escape }}=\sqrt{\frac{GM}{R}}$
$\frac{V_{\text{escape Earth }}}{V_{\text{escape moon }}}=\sqrt{\frac{M_e}{R_e}\times \frac{R_m}{M_m}}$
$=\sqrt{\frac{81}{4}}=\left(\frac{9}{2}\right)$
$\Rightarrow V_{\text{moon }}=\frac{2}{9}\times 11.2=2.48km/s$