The moon's radius is $1/4$ that of the earth and its mass is $1/80$ times that of the earth. If $g$ represents the acceleration due to gravity on the surface of the earth, that on the surface of the moon is

If earth has a mass nine times and radius twice to the of a planet $P$. Then $\frac{v_e}{3} \sqrt{x}\; ms ^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of $P$, where $v_e$ is escape velocity on earth. The value of $x$ is

Consider two spherical planets of same average density. Second planet is $8$ times as massive as first planet. The ratio of the acceleration due to gravity of the second planet to that of the first planet is

Given below are two statements :

Statement$-I:$ Acceleration due to gravity is different at different places on the surface of earth.

Statement$-II:$ Acceleration due to gravity increases as we go down below the earth's surface.

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

Obtain an expression for the variation in effective gravitational acceleration $g'$ with latitude due to earth’s rotation.

If a man at the equator would weigh $(3/5)^{th}$ of his weight, the angular speed of the earth is