Assertion : If a particle moves with a constant velocity, then angular momentum of this particle about any point remains constant.
Reason : Angular momentum has the units of Plank's constant.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is fasle
D. If Assertion is false but Reason is true

Explanation

To solve the given assertion-reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Analyze the Assertion
The assertion states: "If a particle moves with a constant velocity, then angular momentum of this particle about any point remains constant."

1. **Understanding Angular Momentum**: Angular momentum (L) of a particle about a point is given by the formula:
\[ L = m \cdot v \cdot r \cdot \sin(\theta) \]
where:
- \(m\) = mass of the particle,
- \(v\) = velocity of the particle,
- \(r\) = distance from the point to the line of action of the velocity,
- \(\theta\) = angle between the position vector and the velocity vector.

2. **Constant Velocity**: If the particle is moving with a constant velocity, then both the speed (magnitude of velocity) and direction of the velocity remain unchanged.

3. **Differentiation**: Taking the time derivative of angular momentum:
\[ \frac{dL}{dt} = m \left( \frac{dv}{dt} \cdot r \cdot \sin(\theta) + v \cdot \frac{dr}{dt} \cdot \sin(\theta) + v \cdot r \cdot \frac{d(\sin(\theta))}{dt} \right) \]
Since \(v\) is constant, \(\frac{dv}{dt} = 0\). If the distance \(r\) and angle \(\theta\) remain constant, then \(\frac{dr}{dt} = 0\) and \(\frac{d(\sin(\theta))}{dt} = 0\).

4. **Conclusion for Assertion**: Therefore, \(\frac{dL}{dt} = 0\), which implies that the angular momentum \(L\) remains constant. Thus, the assertion is true.

### Step 2: Analyze the Reason
The reason states: "Angular momentum has the units of Planck's constant."

1. **Understanding Units**: Angular momentum has units of:
\[ \text{Angular Momentum (L)} = \text{mass} \times \text{velocity} \times \text{distance} = \text{kg} \cdot \text{m/s} \cdot \text{m} = \text{kg} \cdot \text{m}^2/\text{s} \]

2. **Planck's Constant**: Planck's constant (h) has the units of:
\[ h = \text{kg} \cdot \text{m}^2/\text{s} \]

3. **Conclusion for Reason**: Since the units of angular momentum (kg·m²/s) are indeed the same as the units of Planck's constant, the reason is also true.

### Step 3: Relationship Between Assertion and Reason
While both the assertion and reason are true, the reason does not explain the assertion. The assertion is based on the principles of constant velocity and angular momentum, while the reason discusses the units of angular momentum.

### Final Conclusion
- Assertion: True
- Reason: True
- Relationship: The reason is not the correct explanation of the assertion.

Thus, the correct answer is that both the assertion and reason are true, but the reason is not the correct explanation for the assertion.

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