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NEET2016PhysicsCenter of Mass, Momentum and CollisionActual

A sphere of mass m moving with velocity v hits inelastically with another stationary sphere of same mass. The ratio of their final velocities will be (in terms of e )

Options

  1. Av₁ v₂ = 1+e 1-e
  2. Bv₁ v₂ = 1-e 1+e
  3. Cv₁ v₂ = 1+e 2
  4. Dv₁ v₂ = 1-e 2

Correct answer

B. v₁ v₂ = 1-e 1+e

Step-by-step solution

As coefficient of restitution, e= v₂-v₁ u₁-u₂ = v₂-v₁ u-0 v₂-v₁=e u ...(i) By conservation of momentum, Momentum before collision = Momentum after collision aligned & m u=m v₁+m v₂ & v₁+v₂=u & aligned ...(ii) On solving Eqs. (i) and (ii), we get aligned & v₁= u 2 (1-e) and v₂= u 2 (1+e) & v₁ v₂ = 1-e 1+e & aligned

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