Question:
If n bullets each of mass \(m\) are fired with a velocity \(v\) per second from a machine gun, the force required to hold the gun in position is
If n bullets each of mass \(m\) are fired with a velocity \(v\) per second from a machine gun, the force required to hold the gun in position is
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In continuous mass flow problems, force equals rate of change of momentum: \(F = \dot{m}v\).
Updated On: May 8, 2026
- \((n+1)mv\)
- \(\frac{mv}{n^2}\)
- \(\frac{mv}{n}\)
- \(n^2 mv\)
- \(nmv\)
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The Correct Option is
Solution and Explanation
Concept:
Force is defined as the rate of change of momentum:
\[
F = \frac{dp}{dt}
\]
When bullets are fired continuously, the force on the gun is equal to the rate at which momentum is carried away by the bullets.
Step 1: Understand the situation.
Each bullet has mass \(m\) and velocity \(v\). Number of bullets fired per second = \(n\).
Step 2: Momentum of one bullet. \[ p = mv \]
Step 3: Total momentum per second. Since \(n\) bullets are fired per second: \[ \frac{dp}{dt} = n \times mv \]
Step 4: Force on the gun. \[ F = nmv \]
Step 5: Conclusion. \[ \boxed{nmv} \]
Step 1: Understand the situation.
Each bullet has mass \(m\) and velocity \(v\). Number of bullets fired per second = \(n\).
Step 2: Momentum of one bullet. \[ p = mv \]
Step 3: Total momentum per second. Since \(n\) bullets are fired per second: \[ \frac{dp}{dt} = n \times mv \]
Step 4: Force on the gun. \[ F = nmv \]
Step 5: Conclusion. \[ \boxed{nmv} \]
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