Physics - Gravitation Question with Solution | TestHub

The potential energy at the midpoint is $\left(-\frac{Gm{m}_0}{d/2}-\frac{GM{m}_0}{d/2}\right)$ And suppose $\left(\frac{m_0{V}^2}{2}\right)$ kinetic energy is required to just send the particle to infinity. On considering energy conservation, i.e., initial total energy is equal to the final total energy: $\begin{array}{rl}& \left(-\frac{Gm{m}_0}{d/2}-\frac{GM{m}_0}{d/2}\right)+\left(\frac{m_0{V}^2}{2}\right)=0\\ & \Rightarrow V^2=\frac{4G}{d}(M+m)\\ & \Rightarrow V=2\sqrt{\frac{G(M+m)}{d}}\end{array}$