A uniform circular disc of radius R oscillates in a vertical plane about a horizontal axis, its minimum time period is πB2Rg. The value of B is _______.

The time period of a physical pendulum (or compound pendulum) is minimum when the distance between point of suspension and COM (i.e. l) is equal to the radius of gyration about its COM i.e. l = k.The moment of inertia of a disc about an axis perpendicular to its plane and passing through its COM isI=mk2=12mR2⇒k=R2 T=2πmk2+l2mgl⇒ Tmin=2πR22+R22gR/2⇒Tmin=2π2Rg=π42Rg⇒ B=4