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