The height above the surface of the earth where acceleration due to gravity becomes $\frac{g}{9}$ is ( $R$ is the radius of the earth,$g$ is the acceleration due to gravity at the surface).

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 from the options given below.

Which of the following statements is true?

$A$ tunnel is dug along a diameter of the Earth. If $M_e$ and $R_e$ are the mass and radius of the Earth respectively,then the force on a particle of mass $m$ placed in the tunnel at a distance $r$ from the center is:

The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $0.5\, m$. If the mean density of the moon is two-thirds that of the earth and the radius is one-quarter that of the earth,what is the maximum vertical distance through which he can jump on the moon and the ratio of the duration of the jump on the moon to that on the earth?

Two particles are projected vertically upwards with the same velocity on two different planets with accelerations due to gravity $g_1$ and $g_2$ respectively. If they fall back to their initial points of projection after lapse of times $t_1$ and $t_2$ respectively,then