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AIIMS 2018 Physics Simple Harmonic Motion Assertion Reason Question

Type: Assertion Reason-conceptual-Medium-Class 11

Assertion: If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes four times. Reason: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic oscillator.

A

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

B

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

C

If assertion is true but reason is false.

D

If both assertion and reason are false

Correct Answer

Option A

Detailed Explanation

When the amplitude AA of a simple harmonic oscillator is doubled, the total energy EE is given by the formula E∝A2E \propto A^2. Therefore, if AA increases to 2A2A, the new energy becomes E′=k(2A)2=4kA2E' = k(2A)^2 = 4kA^2, indicating that the total energy quadruples, confirming the assertion. The reason accurately states that total energy is directly proportional to the square of the amplitude, making it the correct explanation for the assertion.

Option B is incorrect because the reason does explain the assertion. Options C and D are incorrect as both the assertion and reason are true.

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