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Assertion : In x = A cos omega t, x is t...

Assertion : In `x = A cos omega t`, `x` is the displacement measured from extreme position.
Reason : In the above equation `x = A` at time `t = 0`.

A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.

C

If Assertion is true but Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that in the equation \( x = A \cos(\omega t) \), \( x \) is the displacement measured from the extreme position. - In simple harmonic motion (SHM), the displacement \( x \) is actually measured from the mean position (equilibrium position), not from the extreme position. Therefore, this assertion is **false**. 2. **Understanding the Reason**: - The reason states that in the equation \( x = A \cos(\omega t) \), at time \( t = 0 \), \( x = A \). - If we substitute \( t = 0 \) into the equation, we get: \[ x = A \cos(0) = A \cdot 1 = A \] - This means that at \( t = 0 \), the displacement \( x \) is equal to the amplitude \( A \). This is indeed true, but it does not relate to the assertion about measuring from the extreme position. 3. **Conclusion**: - The assertion is **false** because \( x \) is measured from the mean position, not the extreme position. - The reason is **true** because at \( t = 0 \), \( x \) does equal \( A \). - Therefore, the correct answer is that the assertion is false, but the reason is true. ### Final Answer: - Assertion: False - Reason: True
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