A machine gun fires a bullet of mass 25 g with a velocity of 1000 ms\(^{-1}\). If the man holding the gun can exert a maximum force of 100 N on the gun, the maximum number of bullets that he can fire per second is:
Show Hint
- 4
- 12
- 8
- 6
- 3
The Correct Option is A
Solution and Explanation
Step 1: The impulse imparted to the gun by firing one bullet is equal to the change in momentum of the bullet.
The momentum of one bullet is: \[ p = m \times v = 0.025 \times 1000 = 25 \, {kg m/s} \] The maximum force on the gun is \( F = 100 \, {N} \), and the time taken to impart this force for each bullet is: \[ \Delta t = \frac{p}{F} = \frac{25}{100} = 0.25 \, {seconds} \] Thus, the maximum number of bullets fired per second is: \[ {Rate} = \frac{1}{\Delta t} = \frac{1}{0.25} = 4 \]
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