A bullet of mass 100 g is fired from a gun of mass 20 kg with a velocity of 100ms −1. Calculate the velocity of recoil of the gun:

 Given

Mass of bullet =m=100g=100 /1000kg=1/10kg

Velocity of bullet, v=100ms-1

Mass of gun, M=20kg

Find out

We have to determine the velocity of recoil of the gun

Solution

Let us assume the recoil velocity of the guns as V

Before firing,

The system (gun+bullet) is at rest, therefore, initial momentum of the system =0
Final momentum of the system = momentum of bullet + momentum of gun

mv+MV = 1/10 X 100 + 20 V= 10 +20 V

On applying law of conservation of momentum,

Final momentum = Initial momentum

10+20V=0

20V=−10

V=− 10/20 = 0.5ms-1

Negative sign indicates that the direction of recoil velocity of the gun is opposite to the direction of the velocity of the bullet.

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