A machine gun with a mass of 5kg fires a 50g bullet at a speed of 100 ms$^{-1}$. The recoil speed of the machine gun is

Analysis

To solve this problem, we apply the Law of Conservation of Linear Momentum. This law states that in a closed system, the total momentum before an event (firing the gun) is equal to the total momentum after the event.

Concept

The formula for the conservation of momentum is:

Where:

• $m_g$ = mass of the gun
• $v_g$ = recoil velocity of the gun
• $m_b$ = mass of the bullet
• $v_b$ = velocity of the bullet

Since the gun and bullet are initially at rest, the total initial momentum is zero. When fired, the bullet moves in one direction (positive) and the gun recoils in the opposite direction (negative).

Step-by-Step Solution

1. Identify the given values:

• Mass of the gun ($m_g$) = $5\text{ kg}$
• Mass of the bullet ($m_b$) = $50\text{ g} = 0.05\text{ kg}$ (Always convert grams to kilograms!)
• Velocity of the bullet ($v_b$) = $100\text{ ms}^{-1}$
• Recoil velocity of the gun ($v_g$) = ?

2. Set up the equation:

(The negative sign indicates the opposite direction of the recoil)

3. Substitute the values:

4. Solve for $v_g$:

The magnitude of the recoil speed is $1\text{ ms}^{-1}$.

Conclusion

Comparing our result with the provided options, the correct answer is C.

Exam Tip

Always check your units before calculating! A common mistake in JAMB Physics is forgetting to convert grams (g) to kilograms (kg). If you had used 50 instead of 0.05, you would have gotten an answer of 1000, which would lead you to choose the wrong option. Always ensure mass is in kg and velocity is in ms⁻¹.