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) 3m, 6 : 1 (B) 6m, 3 : 1(C) 3m, 1 : 6 (D) 6m, 1 : 6

Answer 1

The required equation to solve this problem :-   v2 = u2-2gh .  v is final speed in this case it is zero, when astronaut jumps and reaches maximum height his speed is zero. u is initial jumping speed. g is acceleration due to gravity and h is the maximum jumping height.

 

If jumping speed on earth and moon are assumed as same, then height is inversely proportional to acceleration due to gravity.

 



now acceleration due to gravity

G - gravitational constant M mass of earth, ρ is mean density, R is radius

 

If we consider 2/3 of earth density as moon's density and 1/2 of earth radius as moon's radius 

then acceleration due to gravity on moon,

gE is acceleration due to gravity on earth

 



Hence the astronaut will jump a height of 6 × 0.5 = 3 m on moon