When a cannon shell explodes in mid air, then identify the incorrect statement

Options

A. (a) the momentum of the system is conserved at the time of explosion
B. (b) the kinetic energy of the system always increases
C. (c) the trajectory of centre of mass remains unchanged
D. (d) None of the above

Answer

To solve the question about the cannon shell explosion and identify the incorrect statement, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Scenario**: A cannon shell explodes in mid-air. We need to analyze the statements related to momentum and kinetic energy during this explosion.

2. **Evaluate the First Statement**:
- **Statement**: "Momentum of a system is conserved at the time of explosion."
- **Analysis**: In the absence of external forces, the momentum of the system (cannon shell) is conserved. Since the explosion occurs in mid-air and there are no external horizontal forces acting on the system, this statement is **correct**.

3. **Evaluate the Second Statement**:
- **Statement**: "The kinetic energy of the system always increases."
- **Analysis**: When the cannon shell explodes, the total kinetic energy of the fragments can either increase or decrease, depending on the nature of the explosion. However, it is not guaranteed that kinetic energy will always increase; it can remain the same or even decrease in some cases. Thus, this statement is **incorrect**.

4. **Evaluate the Third Statement**:
- **Statement**: "Trajectory of the center of mass remains unchanged."
- **Analysis**: The center of mass of the system before and after the explosion follows the same trajectory, assuming no external forces act on it. Therefore, this statement is **correct**.

5. **Conclusion**:
- Based on the evaluations, the incorrect statement is the second one: "The kinetic energy of the system always increases." Therefore, the answer to the question is **Option B**.

### Final Answer:
The incorrect statement is **Option B: The kinetic energy of the system always increases.**