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.

### Step-by-Step Solution:

1. **Understand the Initial Momentum**:
The initial momentum of the body before the explosion can be calculated using the formula:
\[ \text{Initial Momentum} = M \cdot V \]
where \( M \) is the mass of the body and \( V \) is its initial velocity.

2. **After the Explosion**:
After the explosion, the body splits into two equal parts. Therefore, the mass of each part is:
\[ \text{Mass of each part} = \frac{M}{2} \]

3. **Define the Final Velocities**:
Let’s denote the velocity of the first part (which comes to rest) as \( u_1 = 0 \) and the velocity of the second part as \( v \).

4. **Calculate the Final Momentum**:
The total momentum after the explosion can be expressed as:
\[ \text{Final Momentum} = \left(\frac{M}{2} \cdot 0\right) + \left(\frac{M}{2} \cdot v\right) = \frac{M}{2} \cdot v \]

5. **Apply Conservation of Momentum**:
According to the law of conservation of momentum, the initial momentum must equal the final momentum:
\[ M \cdot V = \frac{M}{2} \cdot v \]

6. **Simplify the Equation**:
We can simplify the equation by dividing both sides by \( M \) (assuming \( M \neq 0 \)):
\[ V = \frac{1}{2} \cdot v \]

7. **Solve for \( v \)**:
To find \( v \), we multiply both sides by 2:
\[ v = 2V \]

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