The weight of a body on the earth is $400\,N$. Then weight of the body when taken to a depth half of the radius of the earth will be ............ $N$.

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.

The acceleration due to gravity at a height of $(\sqrt{2}-1) R$ from the surface of the earth is (Acceleration due to gravity on the surface of the earth $= 10 \ m \ s^{-2}$ and $R$ is radius of the earth). (in $m \ s^{-2}$)

$A$ hole is drilled through the Earth along a diameter and a stone is dropped into it. When the stone reaches the center of the Earth,which of the following quantities remains constant?

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).

The time taken by a simple pendulum for one oscillation is $T$ on the earth's surface. Its time period becomes $xT$ when taken to a height $R$ (equal to the earth's radius) above the earth's surface. The value of $x$ is