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Four solid spheres each of diameter sqar...

Four solid spheres each of diameter `sqart5`cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4cm. The moment is `Nxx10^(-4)kg - m^2` , then N is .

Text Solution

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Let the four spheres be A, B, C & D
`I_(XY) = I_1+I_B _ +I_c + I_D = 2I_A + 2I_B`
`=2[(2)/(5)MR^2 + Ma^2]+2[(2)/(5)MR^2]`

`=4xx(2)/(5)MR^2 + Ma^2 = M[(8)/(5)R^2 + 2(a)^2]`
`=0.5 [(8)/(5)xx((sqrt5)/(2))^2 + 2xx8]xx10^(-4)`
`=0.5 [2+16]xx10^(-4) = 9xx10^(-4)`
`:. N = 9`
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