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WB JEE Medical WB JEE Medical Solved Paper-2006

  • question_answer
    A weightless thread can bear tension upto 37 N. 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 \[g=10\,\text{m}{{\text{s}}^{-2}},\]         then the maximum angular velocity of the stone will be:

    A)  \[2\,\text{rad}\,{{s}^{-1}}\]                       

    B)  \[4\,\text{rad}\,{{s}^{-1}}\]

    C)  \[8\,\text{rad}\,{{s}^{-1}}\]                       

    D)  \[16\,\text{rad}\,{{s}^{-1}}\]

    Correct Answer: B

    Solution :

                     Maximum tension in the thread is given by \[{{T}_{\max }}=mg+\frac{m{{v}^{2}}}{r}\]                 or            \[{{T}_{max}}=mg+mr{{\omega }^{2}}(\because \,v=r\omega )\]                 or            \[{{\omega }^{2}}=\frac{{{T}_{\max }}-mg}{mr}\]                 Given,                 \[{{T}_{\max }}=37\,N,\,m=500g=0.5kg,\,g=10\,m{{s}^{-2}},\] \[r=4\,m\] \[\therefore \]  \[{{\omega }^{2}}=\frac{37-0.5\times 10}{0.5\times 4}=\frac{37-5}{2}\] or            \[{{\omega }^{2}}=16\] or            \[\omega =4\,rad\,{{s}^{-1}}\]


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