Consider a physical pendulum consisting of an inverted "T" shaped rigid body made out of two identical, thin, uniform rods of mass M and length L each joined together and hinged at the top point as sh

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Consider a physical pendulum consisting of an inverted "T" shaped rigid body made out of two identical, thin, uniform rods of mass $M$ and length $L$ each joined together and hinged at the top point as shown, free to rotate in a vertical plane about an axis perpendicular to the plane of the figure. The time period for 'small' angular oscillations is :

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Ans. (D) Use direct formula T = 2 π Mgy CM ​ I ​ ​ where I is the moment of inertia about the axis of rotation at the hinge, M the total mass and y ( CM ) the position of the center of mass w.r.t the axis of rotation. Here, i = [ 3 ML 2 ​ ] + [ 12 ML 2 ​ + ML 2 ] = 12 17 ML 2 ​ and total mass = 2 M and y CM ​ = 3 L /4

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