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Question

# Assertion: Average kinetic energy in one oscillation during SHM of a body is 14mω2A2. Reason: Maximum kinetic energy is 12mω2A2.

A
If both assertion and reason are correct and reason is the correct explanation of assertion.
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B
If both assertion and reason are correct but reason is not the correct explanation of assertion.
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C
Assertion is true but reason is false.
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D
Assertion is false but reason is true.
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Solution

## The correct option is B If both assertion and reason are correct but reason is not the correct explanation of assertion.If v=Aωcosωt Then, vmax=Aω ∴ KEmax=12mv2max=12mω2A2 Further, Average kinetic energy<KE>=<12mω2A2cos2ωt> =12mω2A2<cos2ωt> Average value of cos2ωt for one oscillation <cos2ωt>=12 ∴ <KE>=14mω2A2 Here both assertion and reason are true but reason cannot explain the assertion correctly. Hence, option (b) is correct.

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