Question

A gun fires n bullets per minute, each of mass m. If the speed of the bullet is v, then the magnitude of force (in SI unit) of recoil is

• A. $\frac{mnv}{60}$
• B. $mnv$
• C. $mvg$
• D. $\frac{mv}{n}$

Answer 1

The correct option is A $\frac{mnv}{60}$

Number of bullets fired in a minute = n
Number of bullets fired in 1 second = $\frac{n}{60}$
Initial velocity of bullet, u = 0
Final velocity of bullet = v
Change in momentum, $\Delta p=mv–mu=mv$ ($\because u=0$)
Rate of change of momentum in firing $\frac{n}{60}$ bullets = $\frac{mnv}{60}$
Thus, magnitude of force of recoil of the gun:
F = |Rate of change of momentum| $=\frac{mnv}{60}$
Hence, the correct answer is option (1).