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Question

A bullet of mass 0.01 kg is fired from a gun weighing 2 kg. Calculate the velocity with which the gun recoils if 10 bullets are fired at the same time with a speed of 250 m/s. Consider +ve x axis along the direction of firing.

A
12.5 m/s
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B
1.25 m/s
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C
12.5 m/s
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D
1.25 m/s
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Solution

The correct option is A 12.5 m/s
In the absence of external force on the system of (gun+bullet) along the x direction, conservation of momentum will hold.

Pi=Pf .....(i)

Mass of gun, mgun=2 kg
Mass of bullet, mbullet=0.01 kg
Velocity of bullet vbullet=250 m/s

Momentum of n bullets fired from the gun:
=n×mbullet×vbullet
=10×0.01×250
=25 Ns

Let the recoil velocity of gun be v
Final momentum of system will be:
Pf=25+mgunv

From Eq. (i),
Pi=Pf

0=25+mgunv
v=252=12.5 m/s
Here ve sign represents that the gun will recoil along the ve x axis.

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