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AFMC AFMC Solved Paper-2004

  • question_answer
    When two pendulums X and Y of time period 4s and 4.2 s are made to vibrate simultaneously. They are initially in phase. After how many vibrations, they will be in the same phase?

    A) 25

    B) 30

    C) 35                                          

    D) 21

    Correct Answer: D

    Solution :

    Key Idea: Pendulum having greater time period makes one oscillation less than the other. Time period of pendulum X is 4 s. Time period of pendulum Y is 4.2 s. If X makes n oscillation, then Y makes \[(n-1)\] oscillations. Time taken by X to make n oscillation       \[=4n\]                                                           ...(i) Similarly, time taken by Y to make \[(n-1)\] oscillations \[=4.2(n-1)\]                                                      ?(ii) Equating Eqs. (i) and (ii), we get \[4.2n-4.2=4n\] \[\Rightarrow \]\[4.2n-4n=4.2\] \[\Rightarrow \]\[0.2\,n=4.2\] \[\Rightarrow \]\[n=\frac{4.2}{0.2}\]      \[\therefore \]   \[n=21\]


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