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Statement-I : When an algebraic equation...

Statement-I : When an algebraic equation has been derved, it is advisable to check it for dimensional consistency.
Statement-II : This guarantee that the equation is correct.

A

Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I

B

Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for statement-I

C

Statement-I is true, Statement-II is false.

D

Statement-I is false and Statement-II is true.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the statements provided in the question, we will break down the reasoning behind each statement step by step. ### Step 1: Understanding Statement I **Statement I:** "When an algebraic equation has been derived, it is advisable to check it for dimensional consistency." - **Explanation:** Dimensional consistency means that both sides of an equation must have the same dimensions. This is crucial because if the dimensions do not match, it indicates that there is an error in the derivation of the equation. For example, if we derive an equation for force, we should ensure that the dimensions of mass and acceleration combine to give the dimensions of force. ### Step 2: Understanding Statement II **Statement II:** "This guarantees that the equation is correct." - **Explanation:** While checking for dimensional consistency is a good practice and can help identify errors, it does not guarantee that the equation is correct in all cases. Dimensional analysis can show that the equation is dimensionally consistent, but it does not account for all possible errors, such as numerical coefficients or the underlying physics of the situation. Therefore, while Statement II is related to Statement I, it is not entirely accurate to claim that dimensional consistency guarantees correctness. ### Conclusion - **Final Evaluation:** - Statement I is **true** because checking for dimensional consistency is a necessary step in verifying the correctness of a derived equation. - Statement II is **false** because dimensional consistency does not guarantee that the equation is correct; it only suggests that the dimensions match. ### Final Answer - Statement I is true, and Statement II is false. ---
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