KVPY Sample Paper KVPY Stream-SX Model Paper-7

  • question_answer
    A uniform solid sphere rolls up an inclined plane.
    Now, choose the correct option.

    A) \[h\propto \frac{1}{m}\]             

    B)  \[h\propto \frac{1}{\tan \theta }\]

    C) \[h\propto {{v}^{2}}\]             

    D) \[h\propto \frac{1}{{{r}^{2}}}\]

    Correct Answer: C

    Solution :

    Equating rotational KE at bottom with potential energy at top, we have
    \[\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}I{{\omega }^{2}}=mgh\]
    \[\frac{1}{2}m{{\upsilon }^{2}}+\frac{1}{2}\times \frac{2}{5}m{{r}^{2}}\times \frac{{{\upsilon }^{r}}}{{{r}^{2}}}=mgh\]
    \[{{\upsilon }^{2}}\times \left( \frac{1}{2}+\frac{1}{5} \right)=gh\]
    So, h is independent of mass of ball or angle of inclination.

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