BCECE Engineering BCECE Engineering Solved Paper-2003

  • question_answer A weightless thread can bear tension upto 3.7 kg-wt. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If \[g=10\,m/{{s}^{-2}},\] then the maximum angular velocity of the stone will be:

    A)  4 rad/s                                

    B)         16 rad/s

    C)         \[\sqrt{21}\]rad/s                          

    D)         2 rad/s

    Correct Answer: A

    Solution :

    Key Idea: Tension in thread in vertical circular motion is maximum at the lowest point. At the lowest point of vertical circular motion \[{{T}_{\max }}=mg+\frac{m{{v}^{2}}}{r}\]                 or            \[{{T}_{\max }}=mg+mr{{\omega }^{2}}\]                             ?(i) Given, \[{{T}_{\max }}=3.7\times 10=37N\]                 \[mg=0.5\times 10-5N\] Thus, Eq.(i), becomes  \[37=5+0.5\times 4\times {{\omega }^{2}}\]                 or            \[{{\omega }^{2}}=\frac{37-5}{0.5\times 4}=\frac{32}{2}=16\]                 or            \[\omega =4\,rad/s\]

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