Question:
The radii of the earth and the moon are in the ratio 10 : 1 while acceleration due to gravity on th eearths surface and moons surface are in the ratio 6 : 1. The ratio of escape velocities from earths surface to that of moon surface is
Answer:
The escape velocity is given by ve = √(2gr)
For earth, escape velocity = √ (2 * ge * re)
For moon, escape velocity = √ (2 * gm * rm)
Ratio of escape velocities of earth to moon = √ (2 * ge * re ) /
√ (2 * gm * rm)
= √(1g * 1r / 1/6 g * 1/10 r)
= √(1 (1/60)
= √60 = 7.75
Hence, ratio of escape velocity of earth and moon is 7.75:1
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