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Question

A rifle of mass 5 kg fires a bullet of mass 40 g. The bullet leaves the barrel of the rifle with a velocity 200 ms−1. If the bullet takes 0.004 s to move through the barrel, calculate the recoil velocity of the rifle.

A
3.2 ms1
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B
2 ms1
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C
4 ms1
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D
1.6 ms1
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Solution

The correct option is D 1.6 ms1
Given:
Mass of bullet, mb=40 g=401000 kg=0.04 kg
Mass of rifle, mr=5 kg
Initially, the bullet and the rifle, both were in rest.
Initial velocity of bullet, ub=0
Initial velocity of rifle, ur=0
Final velocity of the bullet, vb=200 ms1

Let recoil velocity of the rifle be vr.
From the law of conservation of momentum, the total initial momentum of the system before firing is equal to the total final momentum of the system after firing.
mbub+mrur=mbvb+mrvr
0=0.04×200+5vr
0=8+5vr
vr=85 ms1=1.6 ms1
Note that the negative sign shows that the rifle recoils in the direction opposite to the bullet after firing.
Therefore, recoil velocity of the rifle is 1.6 ms1.

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