A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin.

Options

A. is zero
B. Remains constant
C. Goes on increasing
D. Goes on decreasing

Answer

To solve the problem of determining the behavior of the angular momentum of a mass \( m \) moving with a constant velocity parallel to the x-axis away from the origin, we can follow these steps:

### Step 1: Understand Angular Momentum
Angular momentum \( L \) with respect to a point (in this case, the origin) is defined as:
\[ L = r \times p \]
where \( r \) is the position vector from the origin to the mass, and \( p \) is the linear momentum of the mass, given by \( p = mv \).

### Step 2: Define the Position and Velocity
Let’s assume the mass \( m \) is moving along a line parallel to the x-axis at a constant height \( y = a \) (where \( a \) is a constant). The position vector \( r \) of the mass can be expressed as:
\[ r = (x, a) \]
where \( x \) is the x-coordinate that changes over time as the mass moves away from the origin.

The velocity \( v \) of the mass is:
\[ v = (v_x, 0) \]
where \( v_x \) is a constant (the speed along the x-axis).

### Step 3: Calculate the Angular Momentum
The angular momentum \( L \) can be calculated as:
\[ L = r \times p = r \times (mv) \]
Substituting for \( r \) and \( p \):
\[ L = (x, a) \times (mv_x, 0) \]

### Step 4: Compute the Cross Product
The cross product in two dimensions can be calculated as:
\[ L = m \cdot v_x \cdot (x \cdot 0 - a \cdot 1) = -m \cdot v_x \cdot a \]
This shows that the angular momentum is:
\[ L = -mav_x \]
The negative sign indicates the direction of angular momentum, but the magnitude is what we are interested in.

### Step 5: Analyze the Result
Since \( m \), \( a \), and \( v_x \) are all constants (the mass, the constant height, and the constant velocity), the angular momentum \( L \) remains constant over time as the mass moves away from the origin.

### Conclusion
Thus, the angular momentum of the mass with respect to the origin remains constant as it moves away with a constant velocity parallel to the x-axis.

### Final Answer
The angular momentum remains constant.

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