Question

# 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?

A
4πGδ3gh
B
4πgh3Gδ
C
3gh4πGδ
D
3Gδ4πgh
Solution
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#### While jumping he converts his initial kineticenergy to potentialenergymv22=mghv=√2ghNow this velocity has to be equal to escape velocity on the sphereEscape velocity=√2GMsR=√8πGR2sδ3By comparing both the velocities we get Radius(Rs)=√3gh4πGδ

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