$A$ particle of mass $m$ moves in a horizontal circle of radius $r$ under the influence of a centripetal force given by $F = -k/r^2$,where $k$ is a constant. Calculate the total energy of the particle.

$A$ satellite is revolving around the Earth with orbital speed $v_0$. If it stops suddenly,the speed with which it will strike the surface of the Earth would be: ($v_e =$ escape velocity of a particle on the Earth's surface)

$A$ satellite moving around the Earth in a circular orbit has kinetic energy '$E$'. What is the minimum amount of energy to be added so that it escapes from the Earth?

$A$ satellite of mass $m$ rotates around the Earth in a circular orbit of radius $R$. If the angular momentum of the satellite is $J$, then its kinetic energy $(K)$ and the total energy $(E)$ of the satellite are:

The ratio of energy required to raise a satellite to a height $h$ above the earth's surface to that required to put it into the orbit at the same height is ($R=$ radius of earth).

$A$ satellite of $10^3 \text{ kg}$ mass is revolving in a circular orbit of radius $2R$. If $\frac{10^4 R}{6} \text{ J}$ of energy is supplied to the satellite,it would revolve in a new circular orbit of radius: (use $g = 10 \text{ m/s}^2$,$R = \text{radius of earth}$) (in $R$)