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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
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B
ML26
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C
ML23
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D
ML2
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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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