Question

A bullet of mass 10 g is fired from a gun of mass 1 kg. If the recoil velocity is 5 m/s, the velocity of the muzzle is

• A. 0.05 m/s
• B. 5 m/s
• C. 50 m/s
• D. 500 m/s

Hint:

Recoil velocity is inversely proportional to mass.

Answer 1

The Correct Option is D

This problem involves the concept of conservation of momentum. According to the law of conservation of momentum, the total momentum before an event is equal to the total momentum after the event, provided no external forces act on the system. In this scenario, the bullet fired from the gun and the gun's recoil are an example of this principle.

Let's denote:

• Mass of the bullet, \(m_b = 10\, \text{g} = 0.01\, \text{kg} \text{. (Note: 1 g = 0.001 kg)}\)
• Mass of the gun, \(m_g = 1\, \text{kg}\)
• Recoil velocity of the gun, \(v_g = 5\, \text{m/s}\)
• Velocity of the bullet (muzzle velocity), \(v_b\) (to be determined)

According to the conservation of momentum:

\(m_g \cdot v_g + m_b \cdot v_b = 0\)

Since the gun and bullet are initially at rest, their combined initial momentum is zero, which means their combined momentum after firing must also be zero. Thus:

\(1 \cdot (-5) + 0.01 \cdot v_b = 0\)

Simplifying the above equation:

\(-5 + 0.01v_b = 0\)

\(0.01v_b = 5\)

\(v_b = \frac{5}{0.01} = 500\, \text{m/s}\)

Thus, the velocity of the muzzle is 500 m/s.

Answer: The correct option is \(500\, \text{m/s}\).