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Question

A metaI rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius R(<L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?

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A
Restoring torque in case A= Restoring torque in case B
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B
Restoring torque in case A< Restoring torque in case B
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C
Angular frequency for case A> Angular frequency for case B.
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D
Angular frequency for case A< Angular frequency for case B.
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Solution

The correct options are
B Restoring torque in case A= Restoring torque in case B
C Angular frequency for case A< Angular frequency for case B.
Restoring torque is same in both cases,
=TI=ω2θ
In case A the moment of Inertia is more as compared to B, So
ωB>ωA
A & D are correct answer

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