Question

A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s, what is the recoil speed of the gun?

• A. 1.6 cm/s
• B. 0.5 cm/s
• C. 2 cm/s
• D. 3 cm/s

Hint:

When a system is initially at rest and there is no external force, the total momentum is conserved. The recoil speed can be calculated using the conservation of momentum.

Answer 1

The Correct Option is A

Using the law of conservation of momentum, the total momentum before firing must equal the total momentum after firing.
Initially, both the shell and the gun are at rest, so the total initial momentum is zero. Let the recoil speed of the gun be \( v_g \).
The momentum of the system after the shell is fired is: \[ m_{\text{shell}} \cdot v_{\text{shell}} + m_{\text{gun}} \cdot v_{\text{gun}} = 0 \] Substituting the given values: \[ 0.020 \cdot 80 + 100 \cdot v_g = 0 \] Solving for \( v_g \): \[ v_g = -\frac{0.020 \cdot 80}{100} = -1.6 \, \text{m/s} \] The negative sign indicates the direction of motion, but the speed is \( 1.6 \, \text{cm/s} \).
Thus, the correct answer is (a).