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JEE Main & Advanced JEE Main Paper (Held On 12 May 2012)

  • question_answer
    A solid sphere is rolling on a surface as shown in figure, with a translational velocity \[v\,m\,{{s}^{-1}}.\] If it is to climb the inclined surface continuing to roll without slipping, then minimum velocity for this to happen is   JEE Main Online Paper (Held On 12 May 2012)

    A) \[\sqrt{2gh}\]                   

    B)                        \[\sqrt{\frac{7}{5}gh}\]

    C)                        \[\sqrt{\frac{7}{2}gh}\]                

    D)                        \[\sqrt{\frac{10}{7}gh}\]

    Correct Answer: D

    Solution :

                    Minimum velocity for a body rolling without slipping\[v=\sqrt{\frac{2gh}{1+\frac{{{K}^{2}}}{{{R}^{2}}}}}\]For solid sphere,\[\frac{{{K}^{2}}}{{{R}^{2}}}=\frac{2}{5}\] \[\therefore \]\[v=\sqrt{\frac{2gh}{1+\frac{{{K}^{2}}}{{{R}^{2}}}}}=\sqrt{\frac{10}{7}gh}\]


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