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Assertion : All equations which are phys...

Assertion : All equations which are physically correct must also be dimensionally correct.
Reason : All equations which are dimensionally correct must also be physically correct.

A

If both assertion and reason are correct and reason is a correct explanation of the assertion.

B

If both assertion and reason are correct and reason is not the correct explanation of the assertion.

C

If assertion is correct but reason is incorrect.

D

If assertion is incorrect but reason is correct.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided. ### Step 1: Analyze the Assertion The assertion states: "All equations which are physically correct must also be dimensionally correct." - **Explanation**: This statement is true. For an equation to be physically correct, it must represent a valid relationship between physical quantities. Since physical quantities have dimensions, any valid equation must also be dimensionally consistent. For example, if we have an equation relating force, mass, and acceleration, it must satisfy the dimensional formula for each quantity involved. ### Step 2: Analyze the Reason The reason states: "All equations which are dimensionally correct must also be physically correct." - **Explanation**: This statement is false. While a dimensionally correct equation may satisfy the dimensional analysis, it does not guarantee that the equation represents a valid physical relationship. For example, the equation \( KE = mv^2 \) is dimensionally correct (as both sides have dimensions of energy), but it is not physically correct. The correct equation for kinetic energy is \( KE = \frac{1}{2} mv^2 \), which is dimensionally and physically correct. ### Step 3: Conclusion Based on the analysis: - The assertion is true. - The reason is false. Thus, the correct option is that the assertion is correct, but the reason is incorrect. ### Final Answer: Assertion is true; Reason is false. ---
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Knowledge Check

  • A : All physically correct equations are dimensionally correct. R : All dimensionally correct equations are physically correct.

    A
    If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
    B
    If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
    C
    If Assertion is true statement but Reason is false, then mark (3).
    D
    If both Assertion and Reason are false statements, then mark (4).
  • Which of the following equations is dimensionally correct?

    A
    pressure = Engery per units volume
    B
    pressure = Energy per units area
    C
    pressure = Momentum `xx` Volume `xx` time
    D
    pressure = Force `xx` area
  • The equaction which is dimensionally correct among the following is

    A
    `v = u + at^(2)`
    B
    `s = ut + at^(3)`
    C
    `s = ut + at^(2)`
    D
    `t = s + av`
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