Simple Harmonic Motion 5 Question 17

22. A metal rod of length L and mass m is pivoted at one end. A thin disc of mass M and radius R(<L) is attached at its centre 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 centre and case B - the disc is free to rotate about its centre. 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?

(2011)

(a) Restoring torque in case A= Restoring torque in case B

(b) Restoring torque in case A< Restoring torque in case B

(c) Angular frequency for case A> Angular frequency for case B

(d) Angular frequency for case A< Angular frequency for case B

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Answer:

Correct Answer: 22. (a,c)

Solution:

  1. τA=τB=mgL2sinθ+MgLsinθ

= Restoring torque about point O.

In case A, moment of inertia will be more. Hence, angular acceleration (α=τ/I) will be less. Therefore, angular frequency will be less.



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