1. Given data

• Mass of bullet: $m = 10\,\text{g} = 0.01\,\text{kg}$
• Speed of bullet on leaving gun: $v = 600\,\text{m/s}$
• Length of barrel: $50\,\text{cm} = 0.5\,\text{m}$
• Mass of gun: $M = 3\,\text{kg}$

We need the impulse supplied to the gun.

2. Use impulse-momentum theorem

Impulse is equal to change in momentum:

$J = \Delta p$

Initially, the gun-bullet system is at rest, so initial momentum is zero.

When the bullet leaves the gun, bullet momentum is

$p_{\text{bullet}} = mv = 0.01 \times 600 = 6\,\text{kg m/s}$

By conservation of momentum, the gun gets equal and opposite momentum:

$p_{\text{gun}} = 6\,\text{kg m/s}$

Therefore, the impulse supplied to the gun is

$J = 6\,\text{N s}$

3. Check options

• A: $12\,\text{N s}$ ❌
• B: $3\,\text{N s}$ ❌
• C: $6\,\text{N s}$ ✅
• D: $36\,\text{N s}$ ❌

4. Note

The barrel length and gun mass are not needed for finding impulse here. They would be useful if asked for recoil velocity or force.

Hence, the correct answer is Option C.