A thin rod of length L and mass M is bent at | vedclass

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(D) The rod is bent at its midpoint into two halves,each of length $l = L/2$ and mass $m = M/2$.Each half acts as a thin rod of length $L/2$ and mass

Vedclass · Accepted Answer

$\frac{ML^2}{12}$

Vedclass · Answer

(D) The rod is bent at its midpoint into two halves,each of length $l = L/2$ and mass $m = M/2$.Each half acts as a thin rod of length $L/2$ and mass $M/2$ rotating about an axis passing through one of its ends.The moment of inertia of a thin rod of mass $m$ and length $l$ about an axis passing through one end and perpendicular to its length is given by $I = \frac{1}{3}ml^2$.Here,$m = M/2$ and $l = L/2$.So,the moment of inertia of one half about the bending point $O$ is $I_{half} = \frac{1}{3} 	imes (M/2) 	imes (L/2)^2 = \frac{1}{3} 	imes \frac{M}{2} 	imes \frac{L^2}{4} = \frac{ML^2}{24}$.Since the two halves are identical and rotate about the same axis passing through $O$,the total moment of inertia is $I_{total} = I_{half} + I_{half} = 2 	imes \frac{ML^2}{24} = \frac{ML^2}{12}$.

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

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