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CMC Medical CMC-Medical VELLORE Solved Paper-2011

  • question_answer
    The moment of inertia of a body about a given axis is 1.2 kg\[{{m}^{2}}\]. Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 \[rad\text{/}{{s}^{2}}\]must be applied about that axis for a duration of

    A)  4 s                                         

    B)  2 s

    C)  8 s                                         

    D)  10 s

    E)  3 s

    Correct Answer: B

    Solution :

                    KE of rotation\[=1500\] \[\frac{1}{2}I{{\omega }^{2}}=1500\] \[\frac{1}{2}\times 1.2\,{{\omega }^{2}}=1500\] \[{{\omega }^{2}}=\frac{1500\times 2}{1.2}=2500\] \[\omega =\sqrt{2500}\]    \[=50\,rad\text{/}s\] From equation of rotational motion \[\omega ={{\omega }_{0}}+\alpha t\] \[50=0+25\times t\]                 \[\therefore \]  \[t=\frac{50}{25}=2\,s\]


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