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Question

Two rods OA and OB of equal length and mass are lying on the xy plane as shown in figure. Let Ix,Iy and Iz be the moment of inertia of the system 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
Iz>Iy>Ix
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Solution

The correct option is B Ix=Iy<Iz
Let OA=OB=l (in metres)
mA=mB=m kg
Moment of inertia of the system about x axis
Ix=2(ml23sin245)
=ml23
(effective length of both rods is lsin45)

Moment of inertia of the system about y axis
Iy=2(ml23cos245)
=ml23

Moment of inertia of the system about z axis
Iz=2(ml23)=2ml23
Ix=Iy<Iz

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