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JEE Main & Advanced Physics Rotational Motion Question Bank Mock Test - Dynamics of Rigid Body

  • question_answer
    A thick walled hollow sphere has outer radius \[R\]. It rolls down an inclined plane without slipping and its speed at the bottom is\[v\]. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom is \[5v/4\]. What is the radius of gyration of the sphere?

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

    B) \[\frac{R}{2}\]

    C) \[\frac{3R}{4}\]           

    D) \[\frac{\sqrt{3}R}{4}\]

    Correct Answer: C

    Solution :

    [c] Case I: \[mgh=\frac{1}{2}m{{v}^{2}}+\frac{1}{2}m{{k}^{2}}{{\omega }^{2}}\] Case II: \[mgh=\frac{1}{2}m\times {{\left( \frac{5v}{4} \right)}^{2}}\] \[\frac{1}{2}m{{k}^{2}}\frac{{{v}^{2}}}{{{R}^{2}}}+\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m\times \frac{25{{v}^{2}}}{16}\] \[\frac{{{k}^{2}}}{{{R}^{2}}}+1=\frac{25}{16}\Rightarrow k=\frac{3R}{4}\]


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