A bullet of mass 20gm is fired from a riffle of mass 8 kg with a velocity of `100m//s`. The velocity of recoil of the rifle is

Options

A. `0.25 m//s`
B. `25 m//s`
C. `2.5 m//s`
D. `250 m//s`

Explanation

To solve the problem of finding the recoil velocity of the rifle when a bullet is fired, we can use the principle of conservation of linear momentum. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the bullet (m_bullet) = 20 grams = 0.02 kg (since 1 gram = 0.001 kg)
- Mass of the rifle (m_rifle) = 8 kg
- Velocity of the bullet (v_bullet) = 100 m/s

2. **Understand the Conservation of Momentum:**
- According to the law of conservation of momentum, the total momentum before firing is equal to the total momentum after firing.
- Initially, both the bullet and the rifle are at rest, so the total initial momentum (p_initial) = 0.

3. **Set Up the Equation:**
- After the bullet is fired, the bullet moves forward with a velocity of 100 m/s, and the rifle recoils backward with a velocity (v_rifle).
- The momentum of the bullet after firing = m_bullet * v_bullet = 0.02 kg * 100 m/s = 2 kg·m/s.
- The momentum of the rifle after firing = m_rifle * v_rifle = 8 kg * v_rifle.

4. **Apply Conservation of Momentum:**
- Since the total initial momentum is equal to the total final momentum:
\[ 0 = (m_bullet * v_bullet) + (m_rifle * v_rifle) \]
- Substituting the values:
\[ 0 = 2 + (8 * v_rifle) \]

5. **Solve for the Recoil Velocity (v_rifle):**
- Rearranging the equation gives:
\[ 8 * v_rifle = -2 \]
- Dividing both sides by 8:
\[ v_rifle = -\frac{2}{8} = -\frac{1}{4} = -0.25 \text{ m/s} \]
- The negative sign indicates that the rifle recoils in the opposite direction to the bullet.

6. **Final Answer:**
- The velocity of recoil of the rifle is **0.25 m/s** (backward).