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Question

A cube of side length a is shown in the figure. At every corner, particles of mass m are present. Find the MOI of system of particles about y−axis.


A
6 ma2
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B
82 ma2
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C
(6+22) ma2
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D
8 ma2
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Solution

The correct option is D 8 ma2
As we can see from the figure,
Distance of particles 2, 3, 8 and 5 from y - axis is a.
and 1 and 4 particles lie on the y axis, hence MOI for 1 and 4 particles is zero.
Distance of particle 6 and 7 from y axis =a2+a2=2a
Hence, moment of inertia of the system is
I=I1+I2+I3+I4+I5+I6+I7+I8
I=0+ma2+ma2+0+ma2+m(2a)2+m(2a)2+ma2
I=8ma2

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