If escape velocity on earth surface is 11.1 ~km / h , then find the escape velocity on moon surface. If mass of moon is (1)/(81) times of mass of earth and radius of moon is (1)/(4) times radius of earth.

Correct answer: A. 2.46 ~km / h Given, Escape velocity on the surface of earth, v_ e =11.1 ~km / h i.e. aligned & v_ e = 2 gR_ e & v_ e = 2 GM_ e R_ e aligned Mass of moon, M_m=(M_e)/(81) Radius of moon, R_ m = R_ e 4 Escape velocity on the surface of moon aligned & v_m= (2 G M_m)/(R_m) = (2 G (M e)/(81))/((R_e)/(4)) & = 2 2 9 GM_ c R_ c =(2)/(9) 2 GM_ c R_ c =(2)/(9) v_ e =(2)/(9) × 11.1=2.46 ~km / h aligned

JIPMER 2019

Exam: JIPMER
Year: 2019
Subject: Physics
Chapter: Gravitation

JIPMER 2019 · Physics · Gravitation

If escape velocity on earth surface is 11.1 ~km / h , then find the...

If escape velocity on earth surface is

11.1 \mathrm{~km} / \mathrm{h}

, then find the escape velocity on moon surface. If mass of moon is

\frac{1}{81}

times of mass of earth and radius of moon is

\frac{1}{4}

times radius of earth.

Options

A $2.46 \mathrm{~km} / \mathrm{h}$
B $3.46 \mathrm{~km} / \mathrm{h}$
C $4.4 \mathrm{~km} / \mathrm{h}$
DNone of these

Correct answer

A. $2.46 \mathrm{~km} / \mathrm{h}$

Step-by-step solution

Given, Escape velocity on the surface of earth,

\mathrm{v}_{\mathrm{e}}=11.1 \mathrm{~km} / \mathrm{h}

i.e.

\begin{aligned} & \mathrm{v}_{\mathrm{e}}=\sqrt{2 \mathrm{gR}_{\mathrm{e}}} \\ & \mathrm{v}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{e}}}} \end{aligned}

Mass of moon,

M_m=\frac{M_e}{81}

Radius of moon,

\mathrm{R}_{\mathrm{m}}=\frac{\mathrm{R}_{\mathrm{e}}}{4} \therefore

Escape velocity on the surface of moon

\begin{aligned} & v_m=\sqrt{\frac{2 G M_m}{R_m}}=\sqrt{\frac{2 G \frac{M e}{81}}{\frac{R_e}{4}}} \\ & =\frac{2 \sqrt{2}}{9} \sqrt{\frac{\mathrm{GM}_{\mathrm{c}}}{\mathrm{R}_{\mathrm{c}}}}=\frac{2}{9} \sqrt{\frac{2 \mathrm{GM}_{\mathrm{c}}}{\mathrm{R}_{\mathrm{c}}}}=\frac{2}{9} \mathrm{v}_{\mathrm{e}}=\frac{2}{9} \times 11.1=2.46 \mathrm{~km} / \mathrm{h} \end{aligned}

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