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There are four solid balls with their ce...

There are four solid balls with their centres at the four comers of a square of side `a`. the mass of each sphere is `m` and radius is `r`. Find the moment of inertia of the system about (i) one of the sides of the square (ii) one of the diagonals of the square.

Text Solution

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`I_(1)=I_(P)+I_(Q)+I_(R)+I_(S)`
`=((2)/(5)mr^(2))=((2)/(5)mr^(2)+ma^(2))+((2)/(5)mr^(2)+ma^(2))+(2)/(5)mr^(2)`
`=(8)/(5)mr^(2)+2ma^(2)`
`I_(1)=I_(P)+I_(Q)+I_(R)+I_(S)`
`=(2)/(5)mr^(2)+((2)/(5)mr^(2)+(ma^(2))/(2))+(2)/(5)mr^(2)+((2)/(5)mr^(2)+(ma^(2))/(2))`
`=(8)/(5)mr^(2)+ma^(2)`
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