In the figure shown two blocks A & B each of mass m having initial separation of 80 cm are placed on smooth horizontal rails. Another block C having mass 2m is attached with A & B with the help of str

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In the figure shown two blocks A & B each of mass m having initial separation of 80 cm are placed on smooth horizontal rails. Another block C having mass 2m is attached with A & B with the help of string of length 0.5 m each. Block C lies 30 cm vertically below the rails. The coefficient of restitutions is $\frac{1}{2}$ for any collision. The maximum separation between block A & B on rails after they collide when system is released from the rest position :-

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When the blocks meet, both strings are vertical, C has dropped 0.5 − 0.3 = 0.2 m and is momentarily at rest. Energy: 2 m g ( 0.2 ) = 2 × 2 1 ​ m u 2 ⇒ u = 2 m / s for each block. Collision with e = 2 ​ 1 ​ : each block rebounds at 2 ​ m / s . Blocks move apart, C rises; at maximum separation all speeds vanish: 2 × 2 1 ​ m ( 2 ​ ) 2 = 2 m g Δ y ⇒ Δ y = 0.1 m. New depth = 0.4 m , so x = 0. 5 2 − 0. 4 2 ​ = 0.3 m ; separation = 2 x = 60 cm . Answer: (C)

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