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Question

# Four thin uniform rods, each of length L and mass M are joined to form a square. The moment of inertia of square about an axis along one of its diagonal is

A
ML26
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B
4ML23
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C
3ML24
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D
2ML23
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Solution

## The correct option is D 2ML23The given condition can be shown as From Perpendicular axis theorem, Iz=Ix+Iy Since, due to symmetry Ix=Iy ⇒ Iz=2Ix or, Ix=Iy=Iz2 Now, for a single rod (say BC), ICOM=ML212 Also, from parallel axis theorem we have Iz=ICOM+Md2 ⇒ Iz=ML212+M×(L2)2=ML23 Similarly, for four rods Iz=4×ML23=4ML23 Hence, the moment of inertia of square about an axis along its one diagonal is Ix=Iy=Iz2=(4ML23)2=2ML23

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