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99 Percentile Qs Bank for JEE MainPhysicsCenter of Mass, Momentum and Collision

A ball of mass 1   kg moving along X -direction collides elastically with a stationary ball of mass m . The first ball (mass = 1   kg ) recoils at right angle to its original direction of motion. If the second ball starts moving at an angle 30 ° with the X -axis, the value of m must be

Options

  1. A0 . 5   kg
  2. B1 . 5   kg
  3. C2 . 5   kg
  4. D2   kg

Correct answer

D. 2   kg

Step-by-step solution

The given data can be diagrammatically represented as below, According to the conservation of linear momentum, ( 1 ) u = m v 2 cos 30 °               . . . 1 ( ∴ Along x - direction) 2 v 1 = m v 2 sin 30 °             . . . 2 ( ∴ therefore Along y - direction) = m v 2 = 2   v 1 On solving 1 and 2 u = 3 v 1 Given, the collision is elastic. ∴ 1 2 u 2 = 1 2 v 1 2 + 1 2   mv 2 2 ⇒   1 2 u 2 = 1 2 u 2 3 + 1

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