Centre of Mass 3 Question 35

38. A 20g bullet pierces through a plate of mass M1=1kg and then comes to rest inside a second plate of mass M2= 2.98kg as shown in the figure. It is found that the two plates initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between M1 and M2. Neglect any loss of material of the plates due to the action of bullet. Both plates are lying on smooth table.

(1979)

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Answer:

Correct Answer: 38. 25

Solution:

  1. Applying conservation of linear momentum twice. We have

mv=M1v1+mv2mv2=(M2+m)v1

Solving Eqs. (i) and (ii), we get

v2v=M2+mM1+M2+m

Substituting the values of m:M1 and M2 we get percentage of velocity retained by bullet

v2v×100=2.98+0.021+2.98+0.02×100=75



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