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

Options

A. Restoring torque in case A= Restoring torque in case (B).
B. restoring torque in case A lt Restoring torque in case (B).
C. Angular frequency for case A gt angular frequency for case (B).
D. Angular frequency for case A lt Angular frequency for case (B).

Answer

A, D

Explanation

`Applying `tau = I prop`
For case (A) : `mg ((l)/(2) sin theta)) + Mg (l sin theta) = I_A prop_A`
(##JMA_CHMO_C10_021_S01##).
For cas (B) : mg((l)/(2) sin theta)) + Mg(l sin theta) = I_B prop_B`
The restoring torque in both the cases is same.
Also` I_A gt I_B :. prop_A lt prop_B`
:. `omega_A lt omega_B`
(a) and (d) are correct options.