Determine the time period of small oscillations for a uniform disc of mass m and radius r that is suspended from a point located at a distance r/2 from its centre.

Step-by-step solution

The time period of a physical pendulum is given by T = 2 I mgd , where I is the moment of inertia about the point of suspension and d is the distance of the centre of mass from the point of suspension. Given d = r 2 . The moment of inertia of the uniform disc about its centre of mass is I_ cm = 1 2 mr^2 . Using the parallel axis theorem, the moment of inertia about the point of suspension is: I = I_ cm + md^2 = 1 2 mr^2 + m ( r 2 )^2 = 1 2 mr^2 + 1 4 mr^2 = 3 4 mr^2 Substituting I and d into the formula for the tim