Question

Q Find Min $U_o$ such that stone will reach other planet.

Answer 1

$\sqrt{\frac{15}{2} \frac{GM_o}{R}}$

Answer 2

The problem is solved by applying the conservation of mechanical energy. The initial energy of the stone (kinetic + potential) launched from the surface of the first planet is equated to its final energy (potential only, as it just reaches the second planet) at the surface of the second planet. The gravitational potential energy is calculated considering the contributions from both celestial bodies. The distance between the centers of the planets is inferred from the diagram as $6R$.