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JEE Main202529 Jan 2025Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

As shown below, bob (A ) of a pendulum having massless string of length ' (R ) ' is released from (60^ ) to the vertical. It hits another bob (B ) of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.)

Options

  1. A( 4 3 Rg )
  2. B( 2 3 Rg )
  3. C( Rg )
  4. D( 1 3 Rg )

Correct answer

D. ( 1 3 Rg )

Step-by-step solution

Velocity of a just before hitting : u = 2 ~g R 2 = gR Just after collision, let velocity of A and B are v ₁ and v₂ respectively by COM: aligned & m u=m v₁+ m 2 v₂ & 2 v₁+v₂=2 u ...(i) & e=1= v₂-v₁ u & v₂-v₁=u..(ii) aligned From (i) -(ii) 3 v ₁= u v ₁= u 3 = 1 3 gR

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