Eduprobe
Question:
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 a vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?
Restoring torque in case A = Restoring torque in case B
Restoring torque in case A < Restoring torque in case B
Angular frequency for case A < Angular frequency for case B
Angular frequency for case A > Angular frequency for case B
Solution:
Restoring torque is the same in both cases, τ = Iα = -ω²θ. In case A, the moment of inertia is more compared to B. So ωB > ωA. A and D are the correct answers.