Centre of Mass 3 Question 8

11. In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50 greater than the original kinetic energy, the magnitude of the relative velocity between the two particles after collision, is

(2018 Main)

(a) v02

(b) v04

(c) 2v0

(d) v02

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Answer:

Correct Answer: 11. (c)

Solution:

  1. From conservation of linear momentum,

mv0+0=mv1+mv2v0=v1+v2 Further, Kf=32K3212mv02=12mv12+12mv22mmv0mRest mv1 Before collision After collision 32v02=v12+v22

Solving Eqs. (i) and (ii),

v1=v02(1+2)v2=v02(12)vrel =v1v2v02[1+21+2]=v02×22=2v0



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