A uniform disc of mass M and radius R is suspended vertically from a pivot at the upper edge of the disc such that it can rotate freely about this point in its own plane. If it is displaced by a small

Question

A uniform disc of mass M and radius R is suspended vertically from a pivot at the upper edge of the disc such that it can rotate freely about this point in its own plane. If it is displaced by a small angle, the disc will execute simple harmonic motion. The period of SHM is 2 π g xR ​ ​ . The value of x is

TestHub · Accepted Answer

Moment of inertia about the pivot at the edge: $I = \frac{1}{2} M R^{2} + M R^{2} = \frac{3}{2} M R^{2}$ .

Physical pendulum: $T = 2 π \frac{I}{M g R} = 2 π \frac{3 R}{2 g}$ .

Comparing with $2 π \frac{x R}{g}$ , $x = 1.5$ .

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