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JEE MainPhysicsCenter of Mass, Momentum and Collision

A small block A of mass m slides down a smooth curved track from a height H = 45L 8 . At the bottom of the track, it collides head-on and elastically with a stationary small block B of mass M . Block B is attached to a fixed support by a light inextensible string of length L to form a pendulum. If block B is to complete a full vertical circle after the collision, the maximum possible value of the mass ratio M m is

Options

  1. A1
  2. B2
  3. C1 2
  4. D4

Correct answer

B. 2

Step-by-step solution

Velocity of block A just before the collision is given by conservation of mechanical energy: u_A = 2gH = 2g ( 45L 8 ) = 45gL 4 = 3 5 2 gL Let the velocity of block B just after the elastic collision be v_B . Since block B is initially at rest, its velocity after a head-on elastic collision is: v_B = 2m m + M u_A For block B to complete a full vertical circle of radius L , its velocity at the lowest point must satisfy: v_B 5gL Substituting the expressions for v_B and u_A : 2m m + M ( 3 5 2 gL ) 5gL 3m m + M 5gL 5gL

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