A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90^ . The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular

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Correct answer: B. (M L^2)/(12)

Since rod is bent at the middle, so each part of it will have same length ((L)/(2)) and mass ((M)/(2)) as shown. Moment of inertia of each part through its one end =(1)/(3)((M)/(2)) ((L)/(2))^2 Hence, net moment of inertia through its middle point O is aligned I & =(1)/(3)((M)/(2))((L)/(2))^2+(1)/(3)((M)/(2))((L)/(2))^2 & =(1)/(3)[(M L^2)/(8)+(M L^2)/(8)]=(M L^2)/(12) aligned

A thin rod of length L and mass M is bent at its midpoint into two...

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