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Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds omega_(1) : omega_(2) : omega_(3) is |
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Answer» `1:1:1` or `OMEGA^(2)=(2K_(R))/I` Since `K_(R)` remains the same for all three configurations, `thereforeomegaprop1/(sqrtl)` LET m be the mass and a be side of each square PLATE In figure 1, MOMENT of inertia about the given AXIS,  `I_(1)=1/12ma^(2)` In figure 2, moment of inertia about the given axis, `I_(2)=1/12ma^(2)`  In figure 3, moment of inertia about the given axis `I_(3)=1/6ma^(2)` `thereforeI_(1):I_(2):I_(3)=1:1:2` As `omegaprop1/(sqrtl)` `thereforeomega_(1):omega_(2):omega_(3)=1:1:1/(sqrt2)=sqrt2:sqrt2:1` |
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