Question

A machine gun of mass 20 kg fires bullets, each of 40 g at the rate of 120 bullets per minute with a speed of $100 m s^{-1}$. The recoil velocity of the gun is:

• A. $0.4 m s^{-1}$
• B. $0.6 m s^{-1}$
• C. $0.8 m s^{-1}$
• D. $0.1 m s^{-1}$

Hint:

Convert mass to kg and time to seconds before calculating momentum!

Answer 1

The Correct Option is A

Step 1: Picture the situation.
A gun of mass 20 kg fires many small bullets forward. By recoil the gun moves backward. We find how fast the gun moves back.

Step 2: Use conservation of momentum.
The total forward momentum given to the bullets each second equals the backward momentum the gun gains each second. So $M_{gun} \times V_{recoil} = (\text{bullets per second}) \times m_{bullet} \times v_{bullet}$.

Step 3: Find the firing rate per second.
The gun fires 120 bullets per minute. Dividing by 60 gives $120/60 = 2$ bullets each second.

Step 4: Write the bullet values in SI units.
Each bullet has mass $40$ g $= 0.040$ kg and speed $100$ m/s.

Step 5: Find the momentum carried by bullets each second.
Momentum per second $= 2 \times 0.040 \times 100 = 8$ kg m/s.

Step 6: Solve for the recoil speed.
This must equal $20 \times V_{recoil}$, so $V_{recoil} = \dfrac{8}{20} = 0.4$ m/s. \[ \boxed{0.4 \ \text{m s}^{-1}} \]