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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    Bullets are fired at angular intervals of 10 s from a moving car A speeding at 36 km/h. At what interval will an officer seated in a car B hear the report when the car B is stationary and car A is moving towards car B. (velocity of sound = 340\[m{{s}^{-1}}\]and velocity of wind, = 20\[m{{s}^{-1}}\])

    A)  9.7 s                                     

    B)  10.2 s

    C)  6.7 s                                     

    D)  5.8 s   

    E)  3.7 s

    Correct Answer: A

    Solution :

                    The apparent frequency \[=n\times \frac{v+{{v}_{a}}-{{v}_{0}}}{v+{{v}_{a}}-{{v}_{s}}}\] Here \[n=\] frequency and \[{{v}_{a}}=\]velocity of air Let\[T\]and\[T\]be the the apparent time periods Then         \[T=\frac{1}{n}\]and \[T=\frac{1}{n}\] \[\therefore \]  \[\frac{1}{T}=\frac{1}{T}\times \frac{v+a-{{v}_{0}}}{v+a-{{v}_{s}}}\] \[\Rightarrow \]               \[T=T\times \left( \frac{v+{{v}_{a}}-{{v}_{s}}}{v+{{v}_{a}}-{{v}_{0}}} \right)\] \[\Rightarrow \]               \[T=10\times \left( \frac{340+20-10}{340+20} \right)\]\[(\because \,{{v}_{0}}=0)\]                      \[=\frac{10\times 350}{360}=\frac{350}{36}=9.7s\]


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