JEE Main & Advanced Physics Two Dimensional Motion Question Bank Non-uniform Circular Motion

  • question_answer
    A stone of mass m is tied to a string and is moved in a vertical circle of radius r making n revolutions per minute.  The total tension in the string when the stone is at its lowest point is               [Kerala (Engg.) 2001]

    A)             \[mg\]

    B)                      \[m(g+\pi \,n\,{{r}^{2}})\]

    C)             \[m(g+\pi \,n\,r)\]

    D)                      \[m\{g+({{\pi }^{2}}\,{{n}^{2}}\,r)/900\}\]

    Correct Answer: D

    Solution :

                    \[T=mg+m{{\omega }^{2}}r=m\{g+4{{\pi }^{2}}{{n}^{2}}r\}\]             \[=m\left\{ g+\left( 4{{\pi }^{2}}{{\left( \frac{n}{60} \right)}^{2}}r \right) \right\}=m\left\{ g+\left( \frac{{{\pi }^{2}}{{n}^{2}}r}{900} \right) \right\}\]


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