A bullet of mass 10 g is fired with a velocity of 100 m/s from a rifle of mass 2.5 kg, the recoil velocity of the rifle is

Options

A. `-0.4" m"//"s"`
B. `+0.4" m"//"s"`
C. `-4" m"//"s"`
D. `+4" m"//"s"`

Answer

To find the recoil velocity of the rifle when a bullet is fired, we can use the principle of conservation of momentum. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a bullet with a mass of 10 grams (0.01 kg) fired from a rifle with a mass of 2.5 kg. We need to find the recoil velocity of the rifle when the bullet is fired with a velocity of 100 m/s.

### Step 2: Convert Units
Convert the mass of the bullet from grams to kilograms:
- Mass of the bullet, \( m_b = 10 \, \text{g} = 10 \times 10^{-3} \, \text{kg} = 0.01 \, \text{kg} \)

### Step 3: Apply 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 rifle and bullet are at rest, so the initial momentum is zero.

Let:
- \( m_r = 2.5 \, \text{kg} \) (mass of the rifle)
- \( v_r \) = recoil velocity of the rifle (which we want to find)
- \( v_b = 100 \, \text{m/s} \) (velocity of the bullet)

The equation for conservation of momentum can be written as:
\[ m_r \cdot v_r + m_b \cdot v_b = 0 \]

### Step 4: Substitute Known Values
Substituting the known values into the equation:
\[ 2.5 \cdot v_r + 0.01 \cdot 100 = 0 \]

### Step 5: Solve for \( v_r \)
Now, simplify and solve for \( v_r \):
\[ 2.5 \cdot v_r + 1 = 0 \]
\[ 2.5 \cdot v_r = -1 \]
\[ v_r = \frac{-1}{2.5} = -0.4 \, \text{m/s} \]

### Step 6: Interpret the Result
The negative sign indicates that the direction of the rifle's recoil is opposite to the direction of the bullet's motion.

### Final Answer
The recoil velocity of the rifle is \( -0.4 \, \text{m/s} \).

---