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/sIn 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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