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The ratio of radii of earth to another p...

The ratio of radii of earth to another planet is `2/3` and the ratio of their mean densitites is `4/5`. IF an astronaut can jump to a maximum height of 1.5m on the earth, with the same effort, the maximum height he can jump on the planet is

A

1m

B

0.8m

C

0.5m

D

1.25m

Text Solution

Verified by Experts

The correct Answer is:
C
Given : `R_e/R_p=2/3`
`d_e/d_p=4/5`
As `MG= g_eR_e^2`
and `M=d_e times 4/3 pi R_e^3`
`therefore d_e times 4/ 3 pi R_e^3 times G= g_e R_e^2`
or `d_e times4/3pi R_e times G=g_e`...(i)
Similarly for planet
`d_p times 4/3 pi R_p G=g_p`.....(ii)
Diving Eq. (i) by Eq . (ii) we get
`g_e/(g_p)= R_e/R_p times d_e/d_p`
`g_e/(g_p)= 2/3 times 4/5=8/15`
=0.5m
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