Statement-1 : Plane angle is a dimensionless quantity.

Statement-2 : All supplementary quantities are dimensionless.

A. Statement 1 and statement 2 is correct and statement 2 is a correct explanation of statement 1.

B. Statement 1 and statement 2 is correct and statement 2 is not the correct explanation of statement 1.

C. Statement 1 is true and statement 2 is false

D. Statement 1 false and statement 2 is true

To tackle the statements you've presented, let's break them down one by one and analyze their validity. This will help us determine the correct answer among the options provided.

Understanding Plane Angles

A plane angle is indeed a dimensionless quantity. This is because it represents the ratio of two lengths: the length of the arc of a circle to the radius of that circle. Since both lengths are measured in the same unit, they cancel each other out, resulting in a dimensionless value. For example, when we say an angle is 30 degrees, we are essentially describing a proportion rather than a physical measurement with dimensions like length or mass.

Exploring Supplementary Quantities

Now, let’s consider the second statement regarding supplementary quantities. Supplementary angles are defined as two angles whose measures add up to 180 degrees. While the concept of supplementary angles is related to angles, it does not imply that all supplementary quantities are dimensionless. In fact, supplementary angles themselves are measured in degrees or radians, which are dimensional units. Therefore, this statement is false.

Evaluating the Statements

• Statement 1: True - Plane angles are dimensionless.
• Statement 2: False - Not all supplementary quantities are dimensionless; angles are measured in degrees or radians.

Conclusion on the Options

Given the analysis above, we can conclude that:

• Statement 1 is true.
• Statement 2 is false.

Thus, the correct answer is C: Statement 1 is true and statement 2 is false.