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Assertion: A dimensionally wrong or inco...

Assertion: A dimensionally wrong or inconsistaent equation must be wrong.
Reason: A dimensionally consistent equation is a exact or a correct equation.

A

if both assertion and reason are true reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation fo assertion.

C

If assertion is true but reaso is false.

D

IF both assertion and reason are false.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the assertion and reason statements, we will analyze each statement step by step. ### Step 1: Analyze the Assertion **Assertion:** A dimensionally wrong or inconsistent equation must be wrong. - **Explanation:** An equation is dimensionally wrong if the dimensions on both sides of the equation do not match. For example, if we consider the equation \( x = vt + a \), where \( x \) is displacement, \( v \) is velocity, \( t \) is time, and \( a \) is acceleration, we can analyze the dimensions: - Displacement \( x \) has the dimension \( [L] \). - Velocity \( v \) has the dimension \( [L T^{-1}] \). - Time \( t \) has the dimension \( [T] \). - Acceleration \( a \) has the dimension \( [L T^{-2}] \). If we try to add \( vt \) (which has dimensions of \( [L] \)) and \( a \) (which has dimensions of \( [L T^{-2}] \)), we see that the dimensions do not match. Therefore, this equation is dimensionally inconsistent, and thus the assertion is correct. ### Step 2: Analyze the Reason **Reason:** A dimensionally consistent equation is an exact or a correct equation. - **Explanation:** An equation is said to be dimensionally consistent when the dimensions on both sides of the equation are the same. However, just because an equation is dimensionally consistent does not guarantee that it is correct in a physical sense. For example, the equation \( F = ma \) is dimensionally consistent, but if the values of \( F \), \( m \), and \( a \) are not properly defined or measured, the equation may not hold true in practice. Therefore, while a dimensionally consistent equation is necessary for correctness, it is not sufficient on its own to ensure that the equation is accurate or valid in a physical context. Thus, the reason is false. ### Conclusion - The assertion is true: A dimensionally wrong or inconsistent equation must be wrong. - The reason is false: A dimensionally consistent equation is not necessarily an exact or correct equation. ### Final Answer The correct option is: **Assertion is true, but the reason is false.** ---

To solve the question regarding the assertion and reason statements, we will analyze each statement step by step. ### Step 1: Analyze the Assertion **Assertion:** A dimensionally wrong or inconsistent equation must be wrong. - **Explanation:** An equation is dimensionally wrong if the dimensions on both sides of the equation do not match. For example, if we consider the equation \( x = vt + a \), where \( x \) is displacement, \( v \) is velocity, \( t \) is time, and \( a \) is acceleration, we can analyze the dimensions: - Displacement \( x \) has the dimension \( [L] \). - Velocity \( v \) has the dimension \( [L T^{-1}] \). ...
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