A satellite of mass $m$ is placed at a distance $r$ from the centre of earth (mass $M$). The mechanical energy of the satellite is

A rocket is fired vertically with a speed of $5\; km s^{-1}$ from the earth’s surface. How far from the earth does the rocket go before returning to the earth ? Mass of the earth $=6.0 \times 10^{24} \;kg ;$ mean radius of the earth $=6.4 \times 10^{6} \;m ; G=6.67 \times 10^{-11} \;N m ^{2} kg ^{2}$

Two masses $m_1\, \& m_2$ are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separation distance of $d$ is :

The energy required to take a satellite to a height $‘h’$ above Earth surface (radius of Earth $= 6.4 \times 10^3\,km$ ) is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2.$ The value of $h$ for which $E_1$ and $E_2$ are equal is

Four spheres each of mass $m$ form a square of side $d$ (as shown in figure). A fifth sphere of mass $M$ is situated at the centre of square. The total gravitational potential energy of the system is