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Question

Three rods each of mass m and length are joined together in the form of an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through centre of mass of the system (G) and perpendicular to the plane of paper?
1021858_cda5b9507b1445968a466559ace99a96.png

A
2m2
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B
m22
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C
m23
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D
m26
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Solution

The correct option is B m22
The centre of mass of equilateral triangle is the centroid of the equilateral triangle.
As shown in figure, OP=L2tan(30o)=L23
Moment of inertia(MOI) of rod about centre of mass, Icm=112mL2
Using parallel axis theorem of MOI, I=Icm+mx2, Where Icm is MOI about centre of mass and x is distance between centre of mass and axis of rotation.
MOI of the system =3(112mL2+m(L23)2)=3×16mL2=mL22

944588_1021858_ans_9b4e96c250b944b99038c5a5aff82935.png

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