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 jump on the moon to that on the earth are

Given below are two statements:

Statement $I:$ Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement $II:$ Acceleration due to earth's gravity is same at a height ' $h$ ' and depth ' $d$ ' from earth's surface, if $h = d$.

In the light of above statements, choose the most appropriate answer form the options given below

What should be the angular speed with which the earth have to rotate on its axis so that a person on the equator would weigh $\frac{3}{5}$ th as much as present?

During motion of a man from equator to pole of earth, its weight will ....... $\%$ (neglect the effect of change in the radius of earth)

If the Earth has no rotational motion, the weight of a person on the equator is $W$. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weight $\frac{3}{4}\,W$ . Radius of the Earth is $6400\, km$ and $g = 10\, m/s^2$

At what depth below the surface of the earth, acceleration due to gravity $g$ will be half its value $1600 \,km$ above the surface of the earth