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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    A uniform sphere of mass m and radius \[r\] rolls without sliding over a horizontal plane, rotating about horizontal axis OA. In the process, centre of sphere moves with velocity \[v\] along a circle of radius\[r\]. Total kinetic energy of the sphere is

    A)  \[7\text{/}10\,m{{v}^{2}}\]                       

    B)  \[m{{v}^{2}}\]

    C)  \[9\text{/}10\,m{{v}^{2}}\]                       

    D)  None of these

    Correct Answer: C

    Solution :

     \[E=\frac{1}{2}\left( \frac{2}{5}m{{r}^{2}} \right){{\left( \frac{v}{r} \right)}^{2}}+\frac{1}{2}\times \left[ \frac{2}{5}m{{r}^{2}}+m{{r}^{2}} \right]\,{{\left( \frac{v}{r} \right)}^{2}}\]     \[=\frac{1}{5}M{{v}^{2}}+\frac{7}{10}M{{v}^{2}}=\frac{9}{10}M{{v}^{2}}\]


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