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JEE Main & Advanced Sample Paper JEE Main Sample Paper-16

  • question_answer
    Figure shows a disc of mass M and radius R M hinged at the centre. A small ball of mass \[\frac{\text{M}}{2}\] is attached to point P with a thread of length 2R and held at rest at position shown. Now, the ball is released to fall under gravity. With what angular speed does the disc start turning when the string becomes taut?

    A) \[\sqrt{\frac{g}{2R}}\]                   

    B) \[\sqrt{\frac{g}{R}}\]

    C) \[\sqrt{\frac{R}{g}}\]                                     

    D) \[\sqrt{\frac{2g}{R}}\]

    Correct Answer: A

    Solution :

    \[v=\sqrt{2gR}\] \[\frac{M}{2}\times \sqrt{2gR}\times R=\frac{1}{2}\times M\times {{R}^{2}}\omega \] \[+=\frac{M}{2}+\frac{M}{2}\times R\times (R\omega )\] \[\Rightarrow \omega =\sqrt{\frac{g}{2R}}\]


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