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Questions  

The moment of inertia of a hollow cubical box of mass M and side a about an axis passing through the centres of two opposite faces is equal to

a
5 M a23
b
5 M a26
c
5 M a212
d
5 M a218

detailed solution

Correct option is D

Taking mass of plate m       Then MI of two plates through which axis is passing  = m a26×2 = ma23M.I. of 4 plates having symmetrical position from the axis.= 4×[ma212+m(a2)2]  = 4×[ma23]Total MI = 4 ma23+ma23 = 5ma23using  m =M6 ⇒MI = 5 Ma218

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