Two particle A and B, of mass `3m and 2m` respectively, are attached to the ends of a light inextensible string which passes over a smooth fixed pulley of negligible mass. After the system is released and A falls through a distance L, it hits a horizontal inelastic table so that its speed is immediately reduced to zero. Assume that B never hits the table or the pulley. Find
(a) the time for which A is resting on the table after the first collision and before it is jerked off,
(b) the difference between the total kinetic energy of the system immediately before A first hits the table and total kinetic energy immediately after A starts moving upwards for the first time. Explain the loss in kinetic energy.

Answer

(a) `sqrt((8)/(5)(L)/(g))`
(b) `(mgL)/(5)`