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Four spheres, each of diameter 2a and ma...

Four spheres, each of diameter `2a and mass M` are placed with their centres on the four corners of a square of side `b`. Calculate one side of the square taken as the axis.

Text Solution

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`I_(1)=2/5 ma^(2), I_(2)=2/5 ma^(2)=2/5 ma^(2)+mb^(2)`
`I_(3)=2/3 ma^(2)+mb^(2), I_(4)=2/5 ma^(2)`
Moment of inertia of the system `I=I_(1)+I_(2)+I_(3)+I_(4)`
`=2/3 ma^(2)+2/5ma^(2)+mb^(2)+2/5ma^(2)+mb^(2)+2/5ma^(2)`
`I=8/5 ma^(2)+2mb^(2)`
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