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.

If the angular speed of the earth is doubled,the value of acceleration due to gravity $(g)$ at the north pole:

If the value of $g$ (acceleration due to gravity) at the Earth's surface is $10 \ m/s^2$,what is its value in $m/s^2$ at the center of the Earth,assuming the Earth is a sphere of radius $R$ meters with uniform mass density?

The acceleration due to gravity at a height $1\, km$ above the earth is the same as at a depth $d$ below the surface of earth. Then $d = $ ......... $km$

The acceleration due to gravity on a planet is $1.96 \, m/s^2$. If it is safe to jump from a height of $3 \, m$ on the Earth,the corresponding height on the planet will be ........ $m$.