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Question

A man can jump 1.5m high on the earth. Calculate the approximate height he might be able to jump on a planet whose density is one-quarter that of the earth and whose radius is one-third of the earth's radius.

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Solution

The work done that man did for jumping 1.5m height in earth.
mgh=mg×1.5
DE Density of earth, RE Radius of earth, in second planet.
Dp=D4,Rp=R3
Volume Vp=43π×R327
Dp=Mpvp
Mp=Dp×vp=DE4×vE27=Me108
g=GMR2=G×M×9108×R2
GME12R2=g12
mg×1.5=m×g12×h
h=12×1.5=18m

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