A physical pendulum pivoted at a point executes angular oscillations. Its mass  m,has its centre of mass at distance r from the point of suspension. If its moment  of inertia is   I, then its angular frequency is 

detailed solution

Correct option is C

For a body executing simple harmonic motion, Restoring torque acting on it after a  small displacement θ , about an axis, τ=−cθWe know that this results in angular oscillations which can be also related τ=Iαby the equation  Equating the above two we get  −cθ=IαWhere for angular oscillations  α=−ω2θHence −cθ=−Iω2θ Simplifying this c=Iω2     Hence  ω=cIFor angular oscillation  ω=cI, where  ω=2πTRestoring torque acting on a rod after a small displacement  θ, about an axis  passing through point of contact O with the curved path,τ=−Mgrsinθ  , for small angles  sinθ≈θ Therefore, τ=−cθ=−Mgrθ Hence  c=Mgr. Substituting this is (1) we get ω=MgrI .