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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

Two masses m 1 and m 2 are connected by a string of length l . They are held in a horizontal plane at a height H above two heavy plates A and B made of different materials placed on the floor. Initially, the distance between the two masses is a < l . When the masses are released they fall freely and collide with the plates simultaneously. The coefficient of restitution for the collision of the first ball-plate pair i

Options

  1. At = 5 2 l 2 - a 2 2 g H
  2. Bt = 5 4 l 2 - a 2 2 g H
  3. Ct = 5 2 l a 2 g H
  4. Dt = 5 4 l a 2 g H

Correct answer

A. t = 5 2 l 2 - a 2 2 g H

Step-by-step solution

The string will become taut when h 1 - h 2 = l 2 - a 2 h 1 = 0 . 8 v t - 1 2 g t 2 h 2 = 0 . 4 v t - 1 2 g t 2 h 1 - h 2 = 0 . 4 v t 0 . 4 v t = l 2 - a 2 , where v = 2 g H t = 5 2 l 2 - a 2 2 g H

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