A metal 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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Angular frequency for case A < Angular frequency for case B

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Angular frequency for case A > Angular frequency for case B

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Restoring torque in case A = Restoring torque in case B

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Restoring torque in case A < Restoring torque in case B

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Solution

The correct option is C Restoring torque in case A = Restoring torque in case B
$ω_{B} = \sqrt{\frac{m g l}{m l^{2}}}; ω_{A} = \sqrt{\frac{m g l}{m l^{2} + \frac{1}{2} m r^{2}}}$

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