Question

If escape velocity on earth surface is $11.1km/hr$ 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, $V_{\text{es }}=11.1km/hr$
$<br/>\begin{array}{l}<br/>M_{\text{moon }}=\frac{1}{81}{M}_{\text{earth }}\\ <br/>R_{\text{moon }}=\frac{1}{4}{R}_{\text{earth }}<br/>\end{array}<br/>$
The escape velocity on Earth is given by,
$<br/>V_{\text{es }}=\sqrt{\frac{2G{M}_c}{-R_v-\cdots }}<br/>$
The escape velocity on Moon is given by,
$<br/>\begin{array}{l}<br/>V_{\text{moon }}=\sqrt{\frac{2G{M}_{\text{moon }}}{R_{\text{mven }}}}\\ <br/>V_{\text{moon }}=\sqrt{\frac{2G{M}_e}{8IX\times \frac{R_e}{4}}}\\ <br/>\Rightarrow \frac{2}{9}\sqrt{\frac{2G{M}_e}{-R_{\tau }}=\frac{2}{9}{V}_{\text{es }}}\\ <br/>\Rightarrow V_{\text{moon }}=\frac{2}{9}\times 11.1=2.46km/Hr<br/>\end{array}<br/>$