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Question

A disc of mass 100 g is kept floating horizontally in the air by firing bullets each of mass 5 g with the same velocity at the same rate of 10 bullets per second. The bullets rebound at the same speed in opposite direction. Then, the velocity of each bullet at the time of impact is: (Take g=10 m/s2)

A
1000 m/s
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B
100 m/s
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C
50 m/s
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D
10 m/s
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Solution

The correct option is D 10 m/s
Mass of the disc md=100 g=0.1 kg
Mass of the bullet mb=5g=0.005 kg

Let the speed of each bullet be v. The bullets rebound at the same speed in the opposite direction.
Hence change in speed of each bullet =v(v)=2v
Change in momentum of bullets per sec = Force applied on the disc
i.e n×mb×2v=md×g
10×0.005×2×v=0.1×10
v=12×0.005×10=10 m/s

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