$T$ is the time period of a simple pendulum 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. Then,the value of $x$ will be:

If the radius of the earth contracts by $2\%$ and its mass remains the same,then the weight of a body at the earth's surface:

For a body of mass $m$,the acceleration due to gravity at a distance $R$ from the surface of the earth is $\frac{g}{4}$. Its value at a distance $\frac{R}{2}$ from the surface of the earth is ($R = \text{radius of the earth}$,$g = \text{acceleration due to gravity at the surface}$)

$A$ tunnel is dug through the centre of the earth. Show that a body of mass $m$ when dropped from rest from one end of the tunnel will execute simple harmonic motion.

At which location on Earth is the effective acceleration due to gravity maximum?

The depth $d$ at which the value of acceleration due to gravity becomes $\frac{1}{n-1}$ times the value at the earth's surface is ($R=$ radius of the earth).