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JEE Main20199 Jan 2019Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Three blocks A , B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M . Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically. The combined mass collides with C , also perfectly inelastically . 5 6 t h of the initial kinetic energy is lost in the whole process. What is the value of M / m ?

Options

  1. A3
  2. B4
  3. C5
  4. D2

Correct answer

B. 4

Step-by-step solution

m v = m + m v ′ m + m v ′ = m + m + M v f ∴ final velocity v f = m 2 m + M v Initial energy = 1 2 m v 2 Final energy = 1 2 2 m + M m v 2 m + M 2 Given that 5 6 1 2 m v 2 = 1 2 m v 2 - 1 2 2 m + M m v 2 m + M 2 1 12 m v 2 = 1 2 m 2 v 2 2 m + M 6 m = 2 m + M M m = 4

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