A small ball of mass m is connected by an inextensible massless string of length l with another ball of mass M = 4m. They are released at t=0 with zero tension in the string from a height h as shown in the figure. The string becomes taut for the first time at t=lngh after the mass M collides with the ground (Assume all collisions to be elastic) . Find value of n .

Before collision, the velocity of each ball is  V=2gh in the same direction.After collision of M with ground, the velocity of M ball is  V=2gh in the opposite direction.Relative acceleration between the two balls is zero and relative velocity of approach is V-(-V)=2V=22gh .∴  The two balls will collide after a time  =relative distancerelative velocity=l22gh.Since the collision is elastic, the velocity of separation is  22gh∴  The string becomes taut after same time  t=l22gh∴  Total time  will be 2t =  l2gh