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BHU PMT BHU PMT (Mains) Solved Paper-2007

  • question_answer
    When a force\[{{F}_{1}}\]acts on a particle, frequency is 6 Hz and when a force\[{{F}_{2}}\]acts, frequency is 8 Hz. What is the frequency when both the forces act simultaneously in same direction?

    A)  12 Hz                                   

    B)  25 Hz

    C)  10 Hz                                   

    D)  5 Hz

    Correct Answer: C

    Solution :

                     Force, \[F=mr{{\omega }^{2}}\] \[=mr\times {{(2\pi n)}^{2}}=4{{\pi }^{2}}mr{{n}^{2}}\] \[\therefore \]  \[F\propto {{n}^{2}}\] where n is the frequency. When forces\[{{F}_{1}}\]and\[{{F}_{2}}\]act on the panicle simultaneously in same direction, then net force                 \[F={{F}_{1}}+{{F}_{2}}\] \[\therefore \]  \[{{n}^{2}}=n_{1}^{2}+n_{2}^{2}\] \[\Rightarrow \]               \[n=\sqrt{n_{1}^{2}+n_{2}^{2}}\] \[\therefore \]  \[n=\sqrt{{{6}^{2}}+{{8}^{2}}}\]                 \[=\sqrt{100}=10\,Hz\]


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