If the density of the Earth increases $4$ times and its radius becomes half of its present value,our weight will

If the radius of the earth were to shrink by $1\%$ with its mass remaining the same,the acceleration due to gravity on the earth's surface would

If the density of the earth is doubled keeping its radius constant,then the acceleration due to gravity will be........ $m/s^2$. $(g = 9.8\,m/s^2)$

$A$ simple pendulum is oscillating with frequency $F$ on the surface of the earth. It is taken to a depth $R/3$ below the surface of the earth ($R =$ radius of earth). The frequency of oscillation at depth $R/3$ is

The length of a seconds pendulum at a height $h=2R$ from the earth's surface will be. (Given: $R =$ radius of earth and acceleration due to gravity at the surface of earth $g = \pi^{2} \ m/s^{2}$)

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other possesses simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.