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There is crater of depth R//100 on the s...

There is crater of depth `R//100` on the surface of the moon (raduis `R`). A projectile is fired vertically upwards from the crater with a velocity, which is equal to the escape velocity `v` from the surface of the moon. The maximum height attained by the projectile, is :

Text Solution

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The correct Answer is:
99.5 R

Total energy at A=Total energy at B
`(KE)_(A)+(PE)_(A)=(PE)_(B)`
`(1)/(2)mxx(2GM)/(R)+[(-GMm)/(2R^(3)){3R^(2)-((99R)/(100))^(2)}]=-(GMm)/(R+h)`
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