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Question

Three identical rods, each of mass m and length l, form an equilateral triangle. Moment of inertia about one of the sides is


A
ml24
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B
ml2
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C
3ml24
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D
ml22
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Solution

The correct option is D ml22
Given, m1=m2=m3=m kg
l1=l2=l3=l m
Moment of inertia of rod AB about axis along BC
IAB=ml23sin260
=ml24
(because, effective length of rod =lsin60)
Similarly,
Moment of inertia of rod AC about axis along BC
IAC=ml23sin260
=ml24

Moment of inertia of rod BC about axis along BC
IBC=0

Total moment of inertia (I)=IAB+IAC+IBC
=ml24+ml24+0=ml22

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