Question

Given mass of the moon is 1/81 of the mass of the earth and corresponding radius is 1/4 of the earth. If escape velocity on the earth surface is 11.2 km/s, the value of same on the surface of the moon is

• A. 0.14 km/s
• B. 0.5 km/s
• C. 2.5 km/s
• D. 5 km/s

Answer 1

Answer: (C)

2.5 km/s

Answer 2

On earth $v _ { e } = \sqrt { \frac { 2 G M } { R } } = 11.2 \mathrm {~km} / \mathrm { s }$

On moon $v _ { m } = \sqrt { \frac { 2 G M \times 4 } { 81 \times R } } = \frac { 2 } { 9 } \sqrt { \frac { 2 G M } { R } }$

$= \frac { 2 } { 9 } \times 11.2 = 2.5 \mathrm {~km} / \mathrm { s }$