1
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Question

# The moment of inertia of a uniform rod of length 2l and mass m about an axis (X−X) passing through its centre and inclined at an angle α=30∘ is

A
ml212
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B
ml23
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C
ml26
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D
ml24
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Solution

## The correct option is A ml212 Mass per unit length of the rod λ=m2l, dm=λdx The perpendicular distance of the element from the given axis is xsinα The desired moment of inertia is dI=(dm)(xsinα)2 I=x=+l∫x=−ldI =l∫−l(m2l.dx)(xsinα)2 =ml23sin2α, Putting the value of α=30o we get, I=ml212 Hence option A is the correct answer

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