Assertion The angular momentum of system always remain constant.
Reason For a system, `tau_(ext)=(dL)/(dt)=0`

Options

A. Both Assertion and Reason are correct, Reason is the coreect expianation of Assertion
B. Bioth Assertion and Reason are Correct but Reason is not the correct expalnation of Assertion
C. Assetion is correct and Reason is incorrect
D. Assertion is incorrect and Reason is correct

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "The angular momentum of a system always remains constant." This is a broad statement that implies that angular momentum is invariant under all conditions. However, this is not true in general. Angular momentum remains constant only when there are no external torques acting on the system.

**Hint:** Consider the conditions under which angular momentum is conserved.

### Step 2: Understand the Reason
The reason states that "For a system, \( \tau_{\text{ext}} = \frac{dL}{dt} = 0 \)." This means that if the net external torque (\( \tau_{\text{ext}} \)) acting on the system is zero, then the rate of change of angular momentum (\( \frac{dL}{dt} \)) is also zero. This implies that angular momentum is constant when there are no external torques.

**Hint:** Recall the relationship between torque and angular momentum.

### Step 3: Analyze the Assertion and Reason Together
- The assertion is false because angular momentum does not always remain constant; it only remains constant when the net external torque is zero.
- The reason is true because it correctly states that if the net external torque is zero, then the angular momentum is constant.

### Step 4: Conclusion
Since the assertion is false and the reason is true, the correct response to the question is that the assertion does not hold true while the reason does.

**Final Answer:** The assertion is false, and the reason is true.