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STATEMENT 1 Method of dimension cannot b...

STATEMENT 1 Method of dimension cannot be used for deriving formula containing trigonometrical ratios
STATEMENT-2 Trigonometrical ratios have no dimension

A

Statement-1 is True , Statement-2 is True ,Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True , Statement-2 is True ,Statement-2 is NOT a correct explanation for Statement-1

C

Statement-1 is True , Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given statements, we will break down the reasoning step by step. ### Step 1: Understanding Statement 1 **Statement 1:** The method of dimensions cannot be used for deriving formulas containing trigonometric ratios. - **Explanation:** The method of dimensional analysis is a technique used to derive relationships between physical quantities based on their dimensions. However, trigonometric ratios (like sine, cosine, and tangent) are dimensionless quantities. This means they do not have any physical dimensions associated with them (length, mass, time, etc.). Since dimensional analysis relies on the dimensions of quantities, it cannot be used to derive formulas that include dimensionless quantities like trigonometric ratios. ### Step 2: Understanding Statement 2 **Statement 2:** Trigonometric ratios have no dimensions. - **Explanation:** Trigonometric ratios are defined as the ratios of sides of a triangle. For example, in a right triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Since these are ratios of lengths, the dimensions cancel out, making trigonometric ratios dimensionless. Therefore, this statement is true. ### Step 3: Conclusion Both statements are true: - Statement 1 is true because dimensional analysis cannot be applied to dimensionless quantities. - Statement 2 is true because trigonometric ratios are indeed dimensionless. Thus, the correct conclusion is that both statements are true, and Statement 2 correctly explains Statement 1. ### Final Answer: Both statements are true. ---
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