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

  • question_answer
    A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions \[{{s}^{-2}}\]is

    A) 25 N

    B) 50 N

    C) 78.5 N

    D) 157 N

    Correct Answer: D

    Solution :

    [d] \[Here\,\alpha =2revolutions/{{s}^{2}}=4\pi \,rad/{{s}^{2}}\](given) \[{{I}_{cylinder}}=\frac{1}{2}M{{R}^{2}}=\frac{1}{2}(50){{(0.5)}^{2}}\] =\[\frac{25}{4}Kg-{{m}^{2}}\]              As \[\tau =I\alpha \,so\,TR=I\,\alpha \]             \[\Rightarrow T=\frac{I\alpha }{R}=\frac{\left( \frac{25}{4} \right)(4\pi )}{(0.5)}N=50\pi N=157N\]


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