Question

Th moment of inertia of a rod of mass $$M$$ and length $$L$$ about an axis passing through on edge of perpendicular to its length will be :-

A
ML212
B
ML26
C
ML23
D
ML2

Solution

The correct option is C $$\dfrac {ML^{2}}{3}$$  Given, Mass of rod $$=M$$  Length of Rod $$=L$$ Distance of rods edge from center $$=\dfrac{L}{2}$$ Moment of inertia of rod at center $${{I}_{c}}=\dfrac{1}{12}M{{L}^{2}}$$ For moment of inertia at edge apply parallel axis theorem. $${{I}_{e}}={{I}_{c}}+M{{\left( \dfrac{L}{2} \right)}^{2}}$$ $$I=\dfrac{1}{12}M{{L}^{2}}+M{{\left( \dfrac{L}{2} \right)}^{2}}=\dfrac{1}{3}M{{L}^{2}}$$ moment of inertia at edge is $$\dfrac{1}{3}M{{L}^{2}}$$ Physics

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