A particle moves on a straight line with a uniform velocity. It's angular momentum

Options

A. is always zero
B. is zero about a point on the straight line
C. is not zero about a point away from the straight line
D. about any given point remains constant

Answer

To solve the problem regarding the angular momentum of a particle moving with uniform velocity in a straight line, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
Angular momentum (L) of a particle is defined as:
\[ L = r \times p \]
where \( r \) is the position vector from the point about which we are calculating angular momentum to the particle, and \( p \) is the linear momentum of the particle given by \( p = mv \) (mass times velocity).

2. **Identifying the Motion**:
The particle is moving in a straight line with uniform velocity \( v \). This means that the velocity vector is constant in both magnitude and direction.

3. **Calculating Angular Momentum at Different Points**:
- **About a Point on the Straight Line**:
If we consider a point \( P \) that lies on the straight line of motion of the particle, the perpendicular distance \( r \) from point \( P \) to the line of motion is zero. Therefore, the angular momentum about point \( P \) is:
\[ L = r \times mv = 0 \times mv = 0 \]
Thus, **angular momentum is zero about a point on the straight line**.

- **About a Point Away from the Straight Line**:
If we consider a point \( Q \) that is not on the straight line, the perpendicular distance \( r \) is non-zero. Hence, the angular momentum can be calculated as:
\[ L = r \times mv \]
Since both \( r \) and \( mv \) are non-zero, the angular momentum \( L \) is also non-zero. Therefore, **angular momentum is not zero about any point away from the straight line**.

4. **Checking for Constancy**:
Since the mass \( m \) and the velocity \( v \) are constant (uniform motion), the angular momentum \( L \) calculated about any point away from the straight line will also remain constant as long as the distance \( r \) remains unchanged. Therefore, **angular momentum about any given point remains constant**.

### Conclusion:
Based on the analysis, we can summarize the answers to the options provided:
- **Option 1**: Incorrect (not always true).
- **Option 2**: Correct (angular momentum is zero about a point on the straight line).
- **Option 3**: Correct (angular momentum is not zero about any point away from the straight line).
- **Option 4**: Correct (angular momentum about any given point remains constant).

### Final Answer:
The correct options are 2, 3, and 4.

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