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A boy can jump to a height h from ground on earth . What should be the radius of a sphere of density δ such that on jumping on it, he escapes out of the gravitational field of the sphere?

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Solution

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mv22=mgh

v=√2gh

Now this velocity has to be equal to escape velocity on the sphere

Escape velocity=√2GMsR=√8πGR2sδ3

By comparing both the velocities we get Radius(Rs)=√3gh4πGδ

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