First slide

Gravitaional potential energy

Question

The mass of the earth is 81 times that of the moon and the radius of the earth is 3 5 times that of the moon' The ratio of the escape velocity on the surface of earth to that on the surface of moon will be

Easy

A

0.2
B

2.57
C

4.81
D

0.39

Solution

We know that,
$v_{es} = \sqrt{\frac{2 GM}{R}}$
So, ${(v_{es})}_{E} = \sqrt{[\frac{2 G \times 81 M}{3 \cdot 5 R}]}$
and ${(v_{es})}_{M} = \sqrt{[\frac{2 G \times M}{R}]}$
$∴ \frac{{(v_{eS})}_{E}}{{(v_{es})}_{M}} = \sqrt{(\frac{81}{3 \cdot 5})} = 4 \cdot 81$

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