A spherical uniform planet is rotating about its axis. The velocity of a point on its equator is $V.$ Due to the rotation of planet about its axis the acceleration due to gravity $g$ at equator is $1/2$ of $g$ at poles. The escape velocity of a particle on the planet in terms of $V.$

Given below are two statements:

Statement $I:$ Rotation of the earth shows effect on the value of acceleration due to gravity $(g)$.

Statement $II:$ The effect of rotation of the earth on the value of $g$ at the equator is minimum and that at the pole is maximum.

In the light of the above statements, choose the correct answer from the options given below.

An iron ball and a wooden ball of the same radius are released from a height $‘h’$ in vacuum. The time taken by both of them to reach the ground is

Assume there are two identical simple pendulum Clocks$-1$ is placed on the earth and Clock$-2$ is placed on a space station located at a height $h$ above the earth surface. Clock$-1$ and Clock$-2$ operate at time periods $4\,s$ and $6\,s$ respectively. Then the value of $h$ is $....km$ (consider radius of earth $R _{ E }=6400\,km$ and $g$ on earth $10\,m / s ^{2}$ )

Weight of a body of mass $m$ decreases by $1\%$ when it is raised to height $h$ above  the Earth's surface. If the body is taken to a depth $h$ in a mine, then its weight will

At a given place where acceleration due to gravity is $‘g’$ $m/{\sec ^2}$, a sphere of lead of density $‘d’$ $kg/{m^3}$ is gently released in a column of liquid of density $'\rho '\;kg/{m^3}$. If $d > \rho $, the sphere will