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Question

A bullet fired horizontally with a speed of 400 m/sec. It strikes a wooden block of mass 2 kg hanging vertically with the help of long string. After striking with bullet, block rises a height of 20 cm. If speed with which bullet emerges out from block is 10 λ then find λ. Mass of bullet is 20 gm. (take g=10 m/s2)

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Solution

Given mass of wooden block M=2kg and mass of bullet , m=20gm=0.02kg
Let speed of wooden block after collision is v. Block rises by h=20cm=0.2m
Using conservation of mechanical energy, KE1+PE1=KE2+PE2
12mv2+0=0+mgh v=2gh=2×10×0.2=2m/s

There are no external force are acting so momentum will be conserved.
Linear momentum before collision = Linear Momentum after collision
0.02×400+2×0=0.02×10λ+2×2
λ=10

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