What is the recoil velocity of a gun having mass equal to 5 kg if a bullet of 25 g acquiress the velocity of 500 m/s after from the gun ?

Options

A. 1.5 m/s
B. 2.5 m/s
C. 3.5 m/s
D. 4 m/s

Answer

To find the recoil velocity of a gun when a bullet is fired, we can use the principle of conservation of momentum. According to this principle, the total momentum before firing is equal to the total momentum after firing.

### Step-by-step Solution:

1. **Identify the masses and velocities**:
- Mass of the bullet (m1) = 25 g = 25 × 10^(-3) kg = 0.025 kg
- Velocity of the bullet (v1) = 500 m/s
- Mass of the gun (m2) = 5 kg
- Recoil velocity of the gun (v2) = ? (This is what we need to find)

2. **Write the conservation of momentum equation**:
The total momentum before firing (which is zero, since neither the gun nor the bullet is moving) must equal the total momentum after firing:
\[ m1 \cdot v1 + m2 \cdot v2 = 0 \]
Rearranging gives:
\[ m1 \cdot v1 = - m2 \cdot v2 \]

3. **Substitute the known values into the equation**:
\[ 0.025 \cdot 500 = - 5 \cdot v2 \]

4. **Calculate the left side**:
\[ 0.025 \cdot 500 = 12.5 \]
So the equation now looks like:
\[ 12.5 = -5 \cdot v2 \]

5. **Solve for v2**:
Divide both sides by -5:
\[ v2 = -\frac{12.5}{5} = -2.5 \text{ m/s} \]
The negative sign indicates that the gun recoils in the opposite direction to the bullet.

6. **Final answer**:
The recoil velocity of the gun is 2.5 m/s in the opposite direction of the bullet.