A particle is moving along a straight line with increasing speed. Its angular momentum about a fixed point on this line :

Options

A. Goes on increasing
B. Goes on decreasing
C. May be increasing or decreasing depending on direction of motion
D. Remains zero

Answer

To solve the problem, we need to analyze the situation of a particle moving along a straight line with increasing speed and determine its angular momentum about a fixed point on that line.

### Step-by-Step Solution:

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 motion,
- \(\theta\) = angle between the position vector and the velocity vector.

2. **Analyzing the Motion**:
- The particle is moving along a straight line.
- The fixed point is also on this line.

3. **Determining the Perpendicular Distance (r)**:
- Since the particle is moving along the line and the fixed point is also on that line, the perpendicular distance \(r\) from the line of motion to the point is zero.
- Therefore, \(r = 0\).

4. **Substituting into the Angular Momentum Formula**:
- Substitute \(r = 0\) into the angular momentum formula:
\[ L = m \cdot v \cdot 0 \cdot \sin(\theta) = 0 \]

5. **Conclusion**:
- Since \(L = 0\), the angular momentum of the particle about the fixed point is zero.

### Final Answer:
The angular momentum of the particle about the fixed point on the line is **0**.

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