Acceleration due to gravity $'g'$ for a body of mass $'m'$ on earth's surface is proportional to (Radius of earth$=R$, mass of earth$=M$)

If earth is supposed to be a sphere of radius R, if $g_{30}$ is value of acceleration due to gravity at latitude of $ 30^\circ$ and g at the equator, the value of $g - {g_{{{30}^o}}}$ is

If earth suddenly stop rotating, then the weight of an object of mass $m$ at equator will $[\omega$ is angular speed of earth and $R$ is its radius]

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

If the value of g at the surface of the earth is $9.8$ $m/{\sec ^2}$, then the value of g at a place $480\, km$ above the surface of the earth will be .......... $m/{\sec ^2}$. (Radius of the earth is $6400\, km$)   

The maximum vertical distance through which a fully dressed astronaut can jump on the earth is $0.5\, m$. If mean density of the moon is two-thirds that of the earth and radius is one quarter that of the earth, the maximum vertical distance through which he can jump on the moon and the ratio of time of duration of jump on the moon to that on the earth are