From a uniform solid spherical planet of radius ‘R’, density  $\rho$, a solid spherical material for radius $\frac{2R}{3}$  is scooped out to leave an eccentric hole as shown. Acceleration due to gravity on the surface of the planet before scooping is ‘g’ and mass of the planet left after scooping is M. A particle of same mass M is kept at the end (at common tangent of the eccentric hole as shown in the figure and the system is released from rest. Assuming head-on elastic collision between particle and planet and Newton's law of gravitation to be valid, the particle comes back to the initial position for the first time after a time  $\sqrt{kR}$ where ‘k’ is a constant find value of ‘5k’.  (Take ‘g’ on surface on planet before material is scooped out as  $10m/s^2$)