Three equal masses `m` are rigidly connected to each other by massless rods of length `l` forming and equilateral triangle, as shown above. The assembly is to be given an angular velocity `omega` about an axis perpendicular to the triangle. For fixed `omega`, what is the ratio of the kinetic energy of the assembly for an axis through `B t` compared with that for an axis through `A`.
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Answer

`2`

Explanation

`I_(A) =m((l)/(sqrt(3)))^(2) xx 3 = ml^(2)`
`I_(B) = ml^(2) + ml^(2) rArr I_(B) = 2ml^(2)`
`KE_(B) = (1)/(2) I_(B) omega^(2) rArr KE_(B) = (1)/(2) (2ml^(2)) omega^(2)`
`KE_(A) = (1)/(2) I_(A) omega^(2) rArr KE_(A) = (1)/(2) (ml^(2)) omega^(2)`
`(KE_(B))/(KE_(A)) = ((1)/(2) (2ml^(2))omega^(2))/((1)/(2) (ml^(2)) omega^(2)) = (2)/(1)`.