Question

A machine gun of mass 12 kg fires 25 g bullets at the rate of 4 bullets per second with a velocity of 500 m $s^{-1}$. What force must be applied to the gun to hold it in position?

• A. 20 N
• B. 12.5 N
• C. 50 N
• D. 75 N

Answer 1

The correct option is C 50 N

Change in momentum of one bullet in one second $\Delta P_1=m_{bullet}{u}_{bullet}-0$

$⟹\Delta P_1=0.025\times 500=12.5kgm/s$

Number of bullets fired in one second $n=4$

Thus total change in momentum in one second $\Delta P_{total}=n\Delta P_1=4\times 12.5=50kgm/s$

Force applied to hold the gun is equal to the magnitude of change in momentum of the bullets in one second.

$⟹F=50N$