The time period of a simple pendulum on the surface of the earth is $T$. The height above the surface of the earth at which the time period of the pendulum becomes $2T$ is (Radius of the earth $= 6400 \text{ km}$) (in $\text{ km}$)

$A$ body of weight $W$ is projected vertically upwards from the Earth's surface to reach a height above the Earth which is equal to nine times the radius of the Earth. The weight of the body at that height will be

How does the force of gravity $F$ vary inside the Earth at a distance $r$ from the center,where $r < R_e$?

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.

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

As we go from the equator to the poles,the value of $g$