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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 true and the Reason is correct explanation of the Assertion.

B

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

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the assertion and reason provided in the question, we will break down the statements step by step. ### Step 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. **Explanation**: - In simple harmonic motion (SHM), the displacement \( x \) represents how far the object is from its equilibrium position at any given time \( t \). - The extreme positions in SHM are the maximum displacements from the equilibrium position, which are \( +A \) and \( -A \). - Therefore, the assertion is correct because \( x \) is indeed measured from the extreme positions. ### Step 2: Understanding the Reason The reason states that in the equation \( x = A \cos(\omega t) \), \( x = A \) at time \( t = 0 \). **Explanation**: - At \( t = 0 \), substituting into the equation gives: \[ x = A \cos(0) = A \cdot 1 = A \] - This means that at \( t = 0 \), the displacement \( x \) is equal to the amplitude \( A \), which corresponds to one of the extreme positions. - Thus, the reason is also correct. ### Step 3: Connecting the Assertion and Reason Now we need to determine if the reason correctly explains the assertion. - The assertion claims that \( x \) is the displacement from the extreme position, and the reason shows that at \( t = 0 \), the displacement is indeed at one of the extreme positions (specifically at \( x = A \)). - Since both statements are true and the reason provides a valid explanation for the assertion, we conclude that the reason is a correct explanation of the assertion. ### Final Conclusion Both the assertion and reason are true, and the reason correctly explains the assertion. Therefore, the answer to the question is: **Both the assertion and reason are true, and the reason is the correct explanation of the assertion.**
To analyze the assertion and reason provided in the question, we will break down the statements step by step. ### Step 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. **Explanation**: - In simple harmonic motion (SHM), the displacement \( x \) represents how far the object is from its equilibrium position at any given time \( t \). - The extreme positions in SHM are the maximum displacements from the equilibrium position, which are \( +A \) and \( -A \). ...
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