Question

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 thirds 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 time of duration of the jump on the moon to that on the earth are.

• A. 3 m, 6 : 1
• B. 6 m, 3 : 1
• C. 3 m, 1 : 6
• D. 6 m, 1 : 6

Answer 1

Answer: (A)

In terms of density and radius,

$g\alpha \rho R$,

Thus,

$g_m=\frac{2}{3}\frac{1}{4}g=\frac{g}{6}$

Also, height jumped is

$h=\frac{v^2}{2mg}$

Hence at moon,

$h^{\prime }=\frac{v^2}{2m{g}^{\prime }}=6h=3m$

Also, time taken is

$t=\frac{v}{g}$

Thus,

$\frac{t^{\prime }}{t}=\frac{g}{g^{\prime }}=6$

Answer is option A.