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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 ?
  1. Total momentum of the system is 7 kg ms1
  2. Momentum of 5 kg mass after collision is  5 kg ms1.
  3. Velocity of 5 kg after collision is 1 m/s
  4. 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 ms1.
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)u0=1v+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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