A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u.$ The mass and the radius of the earth are, respectively, $M$ and $R.$  $G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of $u$ so that the particle does not return back to earth, 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

Two satellites, $A$ and $B,$ have masses $m$ and $2\,m$ respectively. $A$ is in a circular orbit of radius $R,$ and $B$ is in a circular orbit of radius $2R$ around the earth. The ratio of their kinetic energies, $K.E._A / K.E._B ,$ is

A satellite of $10^3 \mathrm{~kg}$ mass is revolving in circular orbit of radius $2 \mathrm{R}$. If $\frac{10^4 \mathrm{R}}{6} \mathrm{~J}$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius:

(use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \mathrm{R}=$ radius of earth)

A stationary body on a surface of earth have negative energy -What it indicate (Negative energy indicates that body is bind with earth. If a body give this energy or it will be given positive energy, it goes to at infinity).