A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the speed of the shell is `80 m/s`, the recoil speed of the gun would be

Options

A. 14 m/s
B. 0.012 m/s
C. 0.016 m/s
D. 100 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 the step-by-step solution:

### Step 1: Understand the System
We have a gun and a shell. The mass of the shell (m_shell) is 0.020 kg, and the mass of the gun (m_gun) is 100 kg. The speed of the shell (v_shell) after being fired is 80 m/s.

### Step 2: Apply Conservation of Momentum
According to the law of conservation of momentum, the total momentum before firing the shell is equal to the total momentum after firing the shell.

- Initial momentum (before firing) = 0 (since both the gun and shell are at rest)
- Final momentum (after firing) = momentum of the shell + momentum of the gun

Mathematically, this can be expressed as:
\[ m_{gun} \cdot v_{gun} + m_{shell} \cdot v_{shell} = 0 \]

### Step 3: Set Up the Equation
Substituting the known values into the equation:
- Let \( v_{gun} \) be the recoil speed of the gun (which we need to find).
- The momentum of the shell is positive in the direction of its motion, and the momentum of the gun will be negative (since it recoils in the opposite direction).

Thus, we have:
\[ 100 \cdot v_{gun} + 0.020 \cdot 80 = 0 \]

### Step 4: Solve for the Recoil Speed of the Gun
Rearranging the equation gives:
\[ 100 \cdot v_{gun} = -0.020 \cdot 80 \]
\[ 100 \cdot v_{gun} = -1.6 \]
\[ v_{gun} = \frac{-1.6}{100} \]
\[ v_{gun} = -0.016 \, \text{m/s} \]

### Step 5: Interpret the Result
The negative sign indicates that the gun recoils in the opposite direction to the motion of the shell. Therefore, the recoil speed of the gun is 0.016 m/s in the opposite direction of the shell's motion.

### Final Answer
The recoil speed of the gun is **0.016 m/s**.

---