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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $$0_0$$. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is :


A
00+ML22
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B
00+ML24
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C
00+2ML2
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D
00+ML2
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Solution

The correct option is B $$0_0 + \dfrac{ML^2}{4}$$
Using Parallel Axis Theorem, 
Moment of inertia about an axis passing through one of the rod ends(E) and perpendicular to its length $$=$$[ moment of inertia of a about an axis passing through its midpoint (o) and perpendicular to its length $$+$$ (total mass of the rod $$\times$$ square of distance between points o and E.)]
$$\therefore I_E=I_o+M(\dfrac{L}{2})^2=0_0+\dfrac{ML^2}{4}$$
141722_75611_ans_593cb7174fe04b2787d3d9a3401f4c78.png

Physics

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