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JEE Main & Advanced Physics Rotational Motion Question Bank Self Evaluation Test - System of Particles Rotational Motion

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

    A) 4 seconds

    B) 2 seconds

    C) 8 seconds

    D) 10 seconds

    Correct Answer: B

    Solution :

    [b] \[I=1.2\,kg\,{{m}^{2}},\,{{E}_{r}}=1500J,\] \[\alpha =25rad/{{\sec }^{2}},\,\,\,{{\omega }_{1}}=0,\,t=?\] \[As\,{{E}_{r}}=\frac{1}{2}I{{\omega }^{2}},\,\omega =\sqrt{\frac{2{{E}_{r}}}{I}}\] \[=\sqrt{\frac{2\times 1500}{1.2}}=50rad/\sec \] \[From\,{{\omega }_{2}}={{\omega }_{1}}+\alpha t\] \[50=0+25t,\text{ }t=2\]seconds


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