Question

If escape velocity on earth surface is $11.1 \,km/hr$ then find the escape velocity on moon surface. If mass of moon is $\left(\frac{1}{81}\right)$ times of mass of Earth and radius of moon is $\left(\frac{1}{4}\right)$ times radius of Earth.

• A. 2.46 km/hr
• B. 3.46 km/hr
• C. 4.4 km/hr
• D. None of these

Answer 1

Answer: (A)

Solution Given, $V _{\text {es }}=11.1 km / hr$
$
\begin{array}{l}
M _{\text {moon }}=\frac{1}{81} M _{\text {earth }} \\
R _{\text {moon }}=\frac{1}{4} R _{\text {earth }}
\end{array}
$
The escape velocity on Earth is given by,
$
V_{\text {es }}=\sqrt{\frac{2 G M_{c}}{-R_{v}-\cdots}}
$
The escape velocity on Moon is given by,
$
\begin{array}{l}
V _{\text {moon }}=\sqrt{\frac{2 G M_{\text {moon }}}{R_{\text {mven }}}} \\
V _{\text {moon }}=\sqrt{\frac{2 G M_{e}}{8 IX \times \frac{R_{e}}{4}}} \\
\Rightarrow \frac{2}{9} \sqrt{\frac{2 G M_{e}}{-R_{\tau}}=\frac{2}{9} V _{\text {es }}} \\
\Rightarrow V _{\text {moon }}=\frac{2}{9} \times 11.1=2.46 km / Hr
\end{array}
$