A shell of mass 200g is fired by a gun of mass 100kg. If the muzzle speed of the shell is `80ms^(-1)` , then the rcoil speed of the gun is

Options

A. `16"cms"^(-1)`
B. `8"cms"^(-1)`
C. `8"ms"^(-1)`
D. `16"ms"^(-1)`

Explanation

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 linear momentum. Here’s a step-by-step solution:

### Step 1: Define the Given Values
- Mass of the shell (m) = 200 g = 0.2 kg (convert grams to kilograms)
- Mass of the gun (M) = 100 kg
- Muzzle speed of the shell (v) = 80 m/s

### Step 2: Apply the Principle of Conservation of Linear Momentum
According to the principle of conservation of linear momentum, the total momentum before firing is equal to the total momentum after firing. Before firing, both the gun and shell are at rest, so the total initial momentum is 0.

After firing:
- Momentum of the shell = m * v = 0.2 kg * 80 m/s
- Momentum of the gun = M * V (where V is the recoil speed of the gun)

Setting the total momentum after firing equal to the total momentum before firing gives us:
\[ m \cdot v + M \cdot V = 0 \]

### Step 3: Rearranging the Equation
From the equation above, we can rearrange it to find the recoil speed (V) of the gun:
\[ M \cdot V = - m \cdot v \]
\[ V = - \frac{m \cdot v}{M} \]

### Step 4: Substitute the Values
Now, substitute the known values into the equation:
\[ V = - \frac{0.2 \, \text{kg} \cdot 80 \, \text{m/s}}{100 \, \text{kg}} \]

### Step 5: Calculate the Recoil Speed
Calculating the above expression:
\[ V = - \frac{16 \, \text{kg m/s}}{100 \, \text{kg}} \]
\[ V = -0.16 \, \text{m/s} \]

### Step 6: Interpret the Result
The negative sign indicates that the direction of the recoil speed of the gun is opposite to the direction of the shell's motion. Therefore, the recoil speed of the gun is 0.16 m/s in the direction opposite to that of the shell.

### Final Answer
The recoil speed of the gun is **0.16 m/s** in the opposite direction to that of the shell.

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