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Question

Two rods OA and OB of equal lengths and masses are lying in the xy plane as shown in figure. Let Ix,Iy and Iz be the moments of inertia of both the rods about x,y and z axis respectively. Then,


A
Ix=Iy>Iz
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B
Ix=Iy<Iz
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C
Ix>Iy>Iz
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D
Ix>Iy=Iz
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Solution

The correct option is B Ix=Iy<Iz
Let the mass and length of both rods be m and l respectively.
Moment of inertia of both rods OA and OB about x - axis:
Ix=2[ml23sin2θ]
[where θ=45]
Ix=2[ml23sin245]=ml33
Moment of inertia of both rods OA and OB about y - axis:
Iy=2[ml23cos2θ]
[θ=45o]
Iy=2[ml33cos245]=ml33
Moment of inertia of both rods OA and OB about z - axis :
Iz=2[ml23]=23ml2

So, Ix=Iy=ml23 and Iz=23ml2
Ix=Iy<Iz

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