The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is V, the escape velocity on the moon will be

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Solution

Q.
The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is V, the escape velocity on the moon will be [2024]

1 $V / 3$

2 $V / 4$

3 $V / 12$

4 $V / 6$

Ans.
(1)

$V_{e s c a p e} = \sqrt{\frac{2 G M}{R}}$

$V_{p l a n e t} = \sqrt{\frac{2 G M}{R}} = V$

$V_{M o o n} = \sqrt{\frac{2 G M \times 16}{144 R}} = \frac{1}{3} \sqrt{\frac{2 G M}{R}}$

$V_{M o o n} = \frac{V_{P l a n e t}}{3} = \frac{V}{3}$

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