Statement-1 : Plane angle is a dimensionaless quantity.
Statement-2 : All supplementary quantities are dimensionless.

Options

A. Statement-1 is true and statement -2 is true
B. Statement -1 is true and statement-2 is false
C. Statement-1 is false and statement -2 is true
D. Statement-1 is false and statement -2 is false

Answer

To analyze the statements given in the question, we will evaluate each statement step by step.

### Step 1: Understanding Plane Angle
- **Definition**: A plane angle is formed when two rays meet at a point. It is measured in radians.
- **Unit**: The unit of plane angle is the radian (rad).
- **Dimensional Analysis**: In the SI system, radians are considered dimensionless because they are defined as the ratio of two lengths (arc length to radius). Therefore, the plane angle does not have any physical dimensions associated with it.

**Conclusion for Statement 1**: Plane angle is indeed a dimensionless quantity.

### Step 2: Understanding Supplementary Quantities
- **Definition**: Supplementary quantities are those quantities that are not defined in the SI system but are used in various applications. They include the plane angle and solid angle.
- **Types of Supplementary Quantities**: There are two primary supplementary quantities:
1. Plane angle (already discussed)
2. Solid angle

### Step 3: Analyzing Solid Angle
- **Definition**: A solid angle is the three-dimensional equivalent of a plane angle and is measured in steradians (sr).
- **Unit**: The unit of solid angle is also the steradian, which is dimensionless for the same reason as radians (it is a ratio of areas).
- **Dimensional Analysis**: Just like the plane angle, the solid angle is also dimensionless.

**Conclusion for Statement 2**: Since both the plane angle and solid angle are dimensionless, it follows that all supplementary quantities are dimensionless.

### Final Conclusion
- **Statement 1**: True (Plane angle is a dimensionless quantity).
- **Statement 2**: True (All supplementary quantities, including plane angle and solid angle, are dimensionless).

### Summary
Both statements are correct.

---