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NEET Sample Paper NEET Sample Test Paper-67

  • 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\[\nu \]. If the inclined plane is frictionless and the sphere slides down without rolling, its speed at the bottom is\[5\nu /4\]. 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 :

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


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