Laila and Majnu are on a boat for a picnic. The boat is initially at rest. Laila has a big watermelon which she throws towards Majnu. The man catches the melon and eats half of it. He throws back the remaining half to Laila. She eats the half of the melon that she receives & throws the remaining part to Majnu. Majnu again eats half of what he receives and returns the remaining part back to Laila. This continues till the melon lasts. The two are sitting at the two ends of the boat which has a length L. Combined mass of the boat and the two lovers is `M_(0)` and the mass of the water melon is M. Assume that the boat can move horizontally on water without any resistive force. Find the displacement of the boat when the watermelon gets finished.

Answer

`(2ML)/(3(M_(0)+M))`