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Question:

The maximum vertical distance through which a full dressed astronaut can jump on the earth is 0.5 m. Estimate the maximum vertical distance through which he can jump on the moon, which has a mean density 2/3 rd that of the earth and radius one quarter that of the earth. 6 m, 7.5 m, 1.5 m, 3 m

6 m

1.5 m

3 m

7.5 m

Solution:

The gravitational acceleration on a planet=g=GMR2=G(4/3πR3ρ)R2=G(4/3)πρR∝ρR
Hence the value of g on moon=gm=ge/6
Since the astronaut has energy to jump only upto 0.5m on earth,
Energy=mghe=mgmhm
⇒hm=ge/gmhe=6×he=3m