A body of mass m rises to height $h = R/5$ from the earth's surface, where $R$ is earth's radius. If $g$ is acceleration due to gravity at earth's surface, the increase in potential energy is

The mass of a spaceship is $1000\ kg$. It is to be launched from the earth's surface out into free space. The value of $g$ and $R$( radius of earth) are $10\ m/s^2 $ and $6400\ km$ respectively. The required energy for this work will be

A particle is projected from the mid – point of the line joining two fixed particles each of mass $'m$'. If the separation between fixed particles is $'l$', the minimum velocity of projection of the particle so as to escape is equal to

A body of mass $m$ kg. starts falling from a point $2R$ above the Earth’s surface. Its kinetic energy when it has fallen to a point $‘R’$ above the Earth’s surface [$R-$Radius of Earth, $M-$Mass of Earth, $G-$Gravitational Constant]

A satellite of mass $m$ is in circular orbit of radius $3 R_E$ about earth (mass of earth $M_{E}$, radius of earth $R_{E}$). How much additional energy is required to transfer the satellite to an orbit of radius $9 R_{E}$?