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 of determining the angular momentum of a particle moving along a straight line with increasing speed about a fixed point on this line, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- Consider a particle of mass \( m \) moving along the positive x-axis with increasing speed \( v \).
- Let’s denote a fixed point \( O \) on this line, which is the point about which we want to calculate the angular momentum.

2. **Angular Momentum Formula**:
- The angular momentum \( L \) of a particle about a point is given by the formula:
\[ L = r \times p \]
where \( r \) is the position vector from the point \( O \) to the particle, and \( p \) is the linear momentum of the particle.

3. **Linear Momentum**:
- The linear momentum \( p \) of the particle can be expressed as:
\[ p = mv \]
where \( v \) is the velocity of the particle.

4. **Position Vector**:
- The position vector \( r \) is the distance from the fixed point \( O \) to the particle. If the distance from \( O \) to the particle is \( r \), then \( r \) is directed along the x-axis.

5. **Cross Product**:
- The angular momentum can be rewritten as:
\[ L = r \times (mv) \]
- Since both \( r \) and \( v \) are in the same direction (along the x-axis), the angle \( \theta \) between \( r \) and \( v \) is \( 0^\circ \).

6. **Calculating the Magnitude**:
- The magnitude of the angular momentum can be expressed as:
\[ L = r \cdot mv \cdot \sin(\theta) \]
- Since \( \sin(0^\circ) = 0 \), we have:
\[ L = r \cdot mv \cdot 0 = 0 \]

7. **Conclusion**:
- Therefore, the angular momentum \( L \) of the particle about the fixed point \( O \) is:
\[ L = 0 \]

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