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KVPY2019PhysicsCenter of Mass, Momentum and Collision

A mass M moving with a certain speed V collides elastically with another stationary mass m   . After the collision, the masses M and m move with speeds V ' and u , respectively. All motion is in one dimension. Then,

Options

  1. AV = V ' + v
  2. BV ' = V + v
  3. CV ' = ( V + v ) 2
  4. Dv = V + V '

Correct answer

D. v = V + V '

Step-by-step solution

Collision is elastic, so both linear momentum and kinetic energy are conserved. We have following situation, According to figure, M V = M V ' + m v … ( i ) (linear momentum conservation) 1 2 M V 2 = 1 2 M V 2 + 1 2 m v 2 (kinetic energy conservation) From Eqs. (i) and (ii), we get M V - V ' = m v and M V 2 - V 2 = m v 2 Dividing Eq. (iv) by Eq. (iii), we have M V 2 - V 2 M V - V ' = m v 2 m v or V + V ' = v

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