A body of mass M moving with velocity V explodes into two equal parts. If one comes to rest and the other body moves with velocity v, what would be the value of v ?

Options

A. V
B. `V//sqrt(2)`
C. `4V`
D. 2V

Explanation

To solve the problem, we will use the principle of conservation of momentum. Here's the step-by-step solution:

### Step 1: Understand the initial conditions
A body of mass \( M \) is moving with a velocity \( V \). When it explodes, it splits into two equal parts, each with mass \( \frac{M}{2} \).

### Step 2: Identify the final conditions
After the explosion:
- One part comes to rest, so its velocity is \( 0 \).
- The other part moves with an unknown velocity \( v \).

### Step 3: Apply the conservation of momentum
According to the conservation of momentum, the total momentum before the explosion must equal the total momentum after the explosion.

**Initial momentum**:
\[ \text{Initial momentum} = M \cdot V \]

**Final momentum**:
The final momentum consists of the momentum of the two parts:
- The first part (mass \( \frac{M}{2} \)) that comes to rest contributes \( \frac{M}{2} \cdot 0 = 0 \).
- The second part (mass \( \frac{M}{2} \)) that moves with velocity \( v \) contributes \( \frac{M}{2} \cdot v \).

Thus, the total final momentum is:
\[ \text{Final momentum} = 0 + \frac{M}{2} \cdot v = \frac{M}{2} v \]

### Step 4: Set up the equation
Setting the initial momentum equal to the final momentum gives us:
\[ M \cdot V = \frac{M}{2} v \]

### Step 5: Solve for \( v \)
To isolate \( v \), we can simplify the equation:
1. Divide both sides by \( M \) (assuming \( M \neq 0 \)):
\[ V = \frac{1}{2} v \]
2. Multiply both sides by \( 2 \):
\[ v = 2V \]

### Final Answer
The value of \( v \) is:
\[ v = 2V \]