A 20 g bullet pierces through a plate of mass M1 = 1 kg and then comes to rest inside a second plate of mass M2= 2.98 kg as shown in Fig. 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.
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a
50%
b
25%
c
100%
d
75%
answer is B.
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Detailed Solution
Apply conservation of momentum after piercing M1 :mu= M1v+ mu1After it enters into M2, finally bullet also moves with velocity v, somu1=(M2+m)vhence, mu =(M1+M2+m)vRequired percentage loss, =u−u1u×100=m(u−u1)mu×100=M1v(M1+M2+m)v×100=11+2.98+0.02×100=25%