Question

A bullet of mass $20\ \text{gram}$ is fired from a gun of mass $2.5\ \text{kg}$ with a speed of $750\ \text{m/s}$. The magnitude of recoil velocity of the gun is

• A. $12\ \text{m/s}$
• B. $3\ \text{m/s}$
• C. $6\ \text{m/s}$
• D. $18\ \text{m/s}$

Hint:

In recoil problems, always convert mass into kilograms before applying momentum conservation.

Answer 1

The Correct Option is C

Step 1: Apply law of conservation of momentum.
Initially, the system is at rest, so total momentum is zero.
Step 2: Write momentum balance equation.
\[ m_b v_b = m_g v_g \] Step 3: Substitute given values.
\[ m_b = 20\ \text{g} = 0.02\ \text{kg},\quad v_b = 750\ \text{m/s} \] \[ m_g = 2.5\ \text{kg} \] Step 4: Calculate recoil velocity.
\[ v_g = \dfrac{0.02 \times 750}{2.5} = 6\ \text{m/s} \]