If $R$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2 \mathrm{~m} / \mathrm{s}^2$, then the length of the second's pendulum at a height $h=2 R$ from the surface of earth will be,:

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.

Reason $R $: At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given below

$Assertion$ : An astronaut experience weightlessness in a space satellite.

$Reason$ : When a body falls freely it does not experience gravity

If the radius of the earth be increased by a factor of $5,$ by what factor its density be changed to keep the value of $g$ the same ?

A body weighs $72\; N$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ?