A shell of mass 0.02 kg is fird by a gun of mass 10 kg. If the muzzle speed of the shell is 600 `ms^(-1)`, what is the recoil speed of the gun?

Options

A. 0.12 m/s
B. 0.16 m/s
C. 0.3 m/s
D. 0.4 m/s

Answer

To solve the problem of finding the recoil speed of the gun when a shell is fired, we can use the principle of conservation of momentum. Here's a step-by-step solution:

### Step 1: Understand the Conservation of Momentum
According to the law of conservation of momentum, the total momentum before an event must equal the total momentum after the event. In this case, before the shell is fired, both the gun and the shell are at rest.

### Step 2: Define the Variables
- Mass of the shell (m_shell) = 0.02 kg
- Mass of the gun (m_gun) = 10 kg
- Muzzle speed of the shell (v_shell) = 600 m/s
- Recoil speed of the gun (v_gun) = ?

### Step 3: Write the Momentum Equation
Before firing, the total momentum is zero:
\[ \text{Initial Momentum} = 0 \]

After firing, the momentum of the shell and the gun must balance:
\[ m_{\text{shell}} \cdot v_{\text{shell}} + m_{\text{gun}} \cdot v_{\text{gun}} = 0 \]

### Step 4: Substitute the Known Values
Substituting the known values into the momentum equation:
\[ 0.02 \cdot 600 + 10 \cdot v_{\text{gun}} = 0 \]

### Step 5: Simplify the Equation
Calculating the momentum of the shell:
\[ 12 + 10 \cdot v_{\text{gun}} = 0 \]

### Step 6: Solve for the Recoil Speed of the Gun
Rearranging the equation to solve for \( v_{\text{gun}} \):
\[ 10 \cdot v_{\text{gun}} = -12 \]
\[ v_{\text{gun}} = -\frac{12}{10} \]
\[ v_{\text{gun}} = -1.2 \, \text{m/s} \]

The negative sign indicates that the gun recoils in the opposite direction to the shell.

### Final Answer
The recoil speed of the gun is **1.2 m/s** in the direction opposite to the shell.

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