A bullet of mass 40 g is fired from a gun of mass 10 kg. If velocity of bullet is 400 m/s. then the recoil velocity of the gun wil be

Options

A. `1*6` m/s in the direction of bullet
B. `1*6` m/s opposite to the direction of bullet
C. `1*8` m/s in the direction of bullet
D. `1*8` m/s opposite to the direction of bullet

Answer

To solve the problem of finding the recoil velocity of the gun when a bullet is fired, we will use the principle of conservation of linear momentum. Here are the steps to arrive at the solution:

### Step 1: Understand the problem
We have a bullet of mass \( m_1 = 40 \, \text{g} = 0.04 \, \text{kg} \) (converted to kilograms) fired from a gun of mass \( m_2 = 10 \, \text{kg} \). The velocity of the bullet \( v_1 = 400 \, \text{m/s} \). We need to find the recoil velocity of the gun, denoted as \( v_2 \).

### Step 2: Apply the conservation of momentum
According to the conservation of momentum, the total momentum before firing is equal to the total momentum after firing. Initially, both the gun and the bullet are at rest, so the initial momentum \( p_{\text{initial}} = 0 \).

After the bullet is fired, the momentum of the bullet and the gun can be expressed as:
\[ p_{\text{final}} = m_1 v_1 + m_2 v_2 \]
Setting the initial momentum equal to the final momentum gives us:
\[ 0 = m_1 v_1 + m_2 v_2 \]

### Step 3: Substitute the known values
Substituting the values we have:
\[ 0 = (0.04 \, \text{kg}) (400 \, \text{m/s}) + (10 \, \text{kg}) v_2 \]

### Step 4: Solve for \( v_2 \)
Rearranging the equation gives:
\[ 10 v_2 = - (0.04 \times 400) \]
Calculating the right side:
\[ 10 v_2 = -16 \]
Now, divide both sides by 10:
\[ v_2 = -1.6 \, \text{m/s} \]

### Step 5: Interpret the result
The negative sign indicates that the direction of the recoil velocity of the gun is opposite to the direction of the bullet's velocity.

### Final Answer
The recoil velocity of the gun is \( 1.6 \, \text{m/s} \) in the direction opposite to that of the bullet.

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