IIT-JEE 2011 · Paper 1 · Physics Q34

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PhysicsMultiple correct+4Question 34 of 69

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?

A rod pivoted at the ceiling, displaced from the vertical dotted line, with a disc attached at its centre to the rod's lower end.

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.

Answer and worked solution

Official answer: A, D

Torque. Gravity acts on the same masses at the same positions in both cases: equal restoring torques (A).

Moment of inertia. If the disc can turn freely about its centre, no torque acts on it about that centre, so it does not rotate and contributes only $ML^2$ . If it is fixed to the rod it also contributes $\frac12MR^2$ . Smaller $I$ in case B gives a larger angular frequency (D).

(A), (D)

Topics:Simple and compound pendulum Moment of inertia

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IIT-JEE 2011 · Paper 1, Physics question 34