The maximum vertical distance through which a fully dressed astronaut can jump on the earth is `0.5 m`. If mean density of the Moon is two-third that of the earth and radius is one quarter that of the earth, the maximum vertical distance through which he can jump on the Moon and the ratio of the time of duration of the jump on the Moon to hold on the earth are

Options

A. 1.5m
B. 3m
C. 6m
D. 7.5m

Answer

B

Explanation

The energy spent by the astronaut for jumping on the earth `=mg_(e )h_(e )`
and on the moon it is `= mg_(m)h_(m)`.
Both these energies are equal.
`therefore mg_(e )h_(e )=mg_(m)h_(m)` and `because g = (GM)/(R^(2))`
`therefore (h_(m))/(h_(e))=(g_(e))/(g_(m))=(G.(4)/(3)piR_(e)^(3)rho_(e))/(R_(e)^(2))xx(R_(m)^(2))/(G.(4)/(3)pi R_(m)^(3)rho_(m))`
`= (R_(e))/(R_(m))xx(rho_(e))/(rho_(m))=(4)/(1)xx(3)/(2)=6`
`therefore h_(m)=6xxh_(e)=6xx0.5=3 m`