Statement-I: A body moving in a straight line parallel to Y-axis can have angular momentum.
Statement-II: We can employ the concept of angular momentum only in rotatory motion

Options

A. If both Statement-I and Statement-II are true, and Statement - II is the correct explanation of Statement– I.
B. If both Statement-I and Statement-II are true but Statement - II is not the correct explanation of Statement – I.
C. If Statement-I is true but Statement-II is false.
D. If Statement-I is false but Statement-II is true.

Answer

To analyze the statements regarding angular momentum, we will break down the problem step by step.

### Step 1: Understanding Angular Momentum
Angular momentum (\(L\)) of a particle is defined as the cross product of the position vector (\(r\)) and the linear momentum (\(p\)) of the particle. Mathematically, it can be expressed as:
\[ L = r \times p \]
where \(p = mv\) (mass times velocity).

### Step 2: Evaluating Statement-I
**Statement-I:** A body moving in a straight line parallel to the Y-axis can have angular momentum.

- Consider a particle moving parallel to the Y-axis. Let’s say it has a mass \(m\) and a velocity \(v\) in the positive Y-direction.
- The position vector \(r\) can be taken from the origin to the particle's position. If the particle is at a distance \(d\) along the X-axis, then \(r\) can be represented as \(d\hat{i} + y\hat{j}\).
- The velocity vector \(v\) is directed along the Y-axis, which can be represented as \(v\hat{j}\).
- The angle between \(r\) and \(v\) is \(90^\circ\) (since one is along the X-axis and the other is along the Y-axis).

Using the formula for angular momentum:
\[ L = r \times mv \]
Since \(r\) and \(v\) are perpendicular, we can simplify this to:
\[ L = mv \cdot d \]
Thus, the body does indeed have angular momentum. Therefore, **Statement-I is true.**

### Step 3: Evaluating Statement-II
**Statement-II:** We can employ the concept of angular momentum only in rotatory motion.

- Angular momentum is not limited to rotational motion. It can also exist in translational motion, as shown in Statement-I.
- For example, consider a rolling sphere. It has both translational motion (moving forward) and rotational motion (spinning). The total angular momentum of the sphere is the sum of its translational and rotational angular momentum.
- Therefore, angular momentum can be present in various types of motion: translational, rotational, and rolling.

Thus, **Statement-II is false.**

### Conclusion
- **Statement-I is true.**
- **Statement-II is false.**

The correct answer is that Statement-I is true and Statement-II is false.

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