Q130 / 160 · TS EAMCET 2021 (05 Aug Shift 2) · Physics

Ball P of mass m moving with velocity 'v' collides with another ball Q of mass 2 m, at rest. If vP and vQ are the final velocities of P and Q respectively, after collision, then
(Assume the coefficient of restitution is 1/3)

  • Correct answer
    A
    vQvP=4
  • B
    vPvQ=4
  • C
    vQvP=2
  • D
    vPvQ=2

Solution

From conservation of linear momentum, we have
mv+2m×0=mvP+2mvQ
⇒v=vP+2vQ  ...1

From coefficient of restitution formula, we have
e=13=vQ-vPv-0
⇒vQ-vP=v3  ...2

On dividing 1 by 2, we have
⇒vP+2vQvQ-vP=3
⇒1+2VQvPvQvP-1=3
⇒1+2VQvP=3vQvP-1
⇒1+2VQvP=3vQvP-3
⇒VQvP=4

Hence, the correct answer is option: 'A'.

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