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WB JEE Medical WB JEE Medical Solved Paper-2014

  • question_answer
    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

    A)  \[1:1:1\]

    B) \[\sqrt{2}:\sqrt{2}:1\]

    C)  \[1:\sqrt{2}:1\]

    D)  \[1:2:\sqrt{2}\]

    Correct Answer: B

    Solution :

     We know that \[K=\frac{1}{2}I{{\omega }^{2}}\] where \[K=\]kinetic energy \[I=\]moment of inertia \[\omega =\]angular speed So,       \[\omega \propto \frac{1}{\sqrt{I}}\] \[{{\omega }_{1}}:{{\omega }_{2}}:{{\omega }_{3}}=\frac{1}{\sqrt{{{I}_{1}}}}:\frac{1}{\sqrt{{{I}_{2}}}}:\frac{1}{\sqrt{{{I}_{3}}}}\] \[=\frac{1}{\sqrt{1}}:\frac{1}{\sqrt{1}}:\frac{1}{\sqrt{2}}=\sqrt{2}:\sqrt{2}:1\]


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