An artificial satellite revolves around the earth in circular orbit with a speed $v$. If $m$ is the mass of the satellite, its total energy is

If a missile launched with a velocity less than escape velocity, the sum of its $K.E$. and $P.E$. is always

The kinetic energy required to make a body to move to infinity from the earth's surface is

A spherically symmetric gravitational system of particles has a mass density $\rho =\left\{\begin{array}{l}{\rho }_0 \mathrm{for} r\le R\\ 0 \mathrm{for} r>R\end{array}\right\}$ where ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r\left(0<r<\mathit{\infty }\right)$ from the centre of the system is represented by