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Question

There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius r. Find the moment of inertia of the system about one of the sides of the square.

A
85mr2+2ma2
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B
58mr2+2ma2
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C
mr2+85ma2
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D
mr2+58ma2
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Solution

The correct option is A 85mr2+2ma2

Moment of Inertia(M.I) of two sphere lying on the axis I1=2×25mr2=45mr2

(M.I) of two sphere lying on the edge parallel to the axis of distance a (By using parallel axis theorem)
I2=2(25mr2+ma2)

Total M.I of the system about one of the sides of the square. I=I1+I2=2×25mr2+2(25mr2+ma2)
=85mr2+2ma2

Hence option A is the correct answer.

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