A body at rest breaks into two pieces of equal masses. The parts will move

Options

A. in same direction
B. along different lines
C. in opposite directions with equal speeds
D. in opposite directions with unequal speeds.

Answer

To solve the problem of a body at rest breaking into two equal masses, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a body at rest that breaks into two pieces of equal mass.
- Let the mass of each piece be \( m \).
- Since the body is initially at rest, its initial momentum is zero.

2. **Initial Momentum**:
- The initial momentum \( P_{initial} \) of the body is given by:
\[ P_{initial} = 0 \quad (\text{since the body is at rest}) \]

3. **Final Momentum**:
- After breaking, let the velocities of the two pieces be \( V \) and \( V' \).
- The final momentum \( P_{final} \) of the system can be expressed as:
\[ P_{final} = mV + mV' \]

4. **Applying Conservation of Momentum**:
- According to the law of conservation of momentum, the total momentum before the break must equal the total momentum after the break:
\[ P_{initial} = P_{final} \]
- Therefore, we have:
\[ 0 = mV + mV' \]

5. **Simplifying the Equation**:
- We can factor out \( m \) (assuming \( m \neq 0 \)):
\[ 0 = V + V' \]
- This implies:
\[ V = -V' \]

6. **Interpreting the Result**:
- The equation \( V = -V' \) indicates that the two pieces move in opposite directions with equal speeds.

7. **Conclusion**:
- Thus, the final conclusion is that the two pieces will move in opposite directions with equal speeds.

### Final Answer:
The parts will move in opposite directions with equal speeds.

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