Question

# A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 m/s. Which of the following statements is (are) correct for the system of two masses ?Total momentum of the system is 7 kg ms−1. Momentum of 5 kg mass after collision is  5 kg ms−1.Velocity of 5 kg after collision is 1 m/s. Velocity of 1 kg before collision is 2 m/s.

Solution

## The correct options are B Momentum of 5 kg mass after collision is  5 kg ms−1. C Velocity of 5 kg after collision is 1 m/s. Let initial velocity of 1 kg mass be u and final velocity of 5 kg mass be v. Applying conservation of linear momentum, taking rightward positive m1u1+m2u2=m1v1+m2v2 1×u+0=1×(−2)+5v ⇒u+2=5v    ...(i) Now e=1=vseparationvapproach ⇒v−(−2)u−0=1⇒v+2=u    ...(ii)  Solving (i) and (ii), v=1 m/s & u=3 m/s Momentum of 5 kg mass after collsion =5v=5 kg m/s Also, total momentum of system =m1u1+m2u2 =1×3+0=3 kg m/s

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