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JEE Advanced2008PhysicsCenter of Mass, Momentum and CollisionActual

Two balls, having linear momenta p ₁=p i and p ₂=-p i , undergo a collision in free space. There is no external force acting on the balls. Let p ₁^ and p ₂^ be their final momenta. The following option(s) is/are NOT ALLOWED for any non-zero value of p, a₁, a₂, b₁, b₂, c₁ and c₂

Options

  1. Ap ₁^ =a₁ i +b₁ j +c₁ k , p ₂^ =a₂ i +b₂ j
  2. Bp ₁^ =c₁ k , p ₂^ =c₂ k
  3. Cp ₁^ =a₁ i +b₁ j +c₁ k
  4. Dp ₁^ =a₁ i +b₁ j p ₂^ =a₂ i +b₂ j -c₁ k p ₂^ =a₂ i +b₁ j

Correct answer

A. p ₁^ =a₁ i +b₁ j +c₁ k , p ₂^ =a₂ i +b₂ j

Step-by-step solution

Initial momentum of the system p ₁ + p ₂ =0 Final momentum p ₁^ + p ₂^ should also be zero. Option (b) is allowed because if we putc c₁=-c₂ 0, p ₁^ + p ₂^ will be zero. Similarly, we can check other options. correct options are (a) and (d).

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