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Q.

The ratio of the radius of earth to that of the moon is 10. The ratio of acceleration due to gravity on the earth and on the moon is 6. The ratio of the escape velocity from the earth's surface to that from the moon is :

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a

nearly 8

b

nearly 10

c

nearly 5

d

nearly 6

answer is C.

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Detailed Solution

$Escape velocity, v_{e} = \sqrt{2 gR}$

$For moon, v_{e, moon} = \sqrt{2 gR}$

$For earth, v_{e, moon} = \sqrt{2 \times 6 g \times 10 R}$

$∴ \frac{v_{e} (earth)}{v_{e} (moon)} = \frac{\sqrt{60 (2 gR)}}{\sqrt{2 gR}} = \sqrt{60} ≃ 8$

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The ratio of the radius of earth to that of the moon is 10. The ratio of acceleration due to gravity on the earth and on the moon is 6. The ratio of the escape velocity from the earth's surface to that from the moon is :