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AIIMS AIIMS Solved Paper-2002

  • question_answer
    The velocities of sound at same temperature in two monoaromic gases densities \[{{k}_{1}}\] and \[{{F}_{1}}=-{{k}_{1}}{{y}_{1}}\] are \[{{F}_{2}}=-{{k}_{2}}{{y}_{2}}\]and \[{{k}_{2}}\] respectively, if\[{{k}_{1}}\], then, the value of \[{{k}_{2}}{{F}_{1}}+{{k}_{1}}{{F}_{2}}=-{{k}_{1}}{{k}_{2}}({{y}_{1}}+{{y}_{2}})=-{{k}_{1}}{{k}_{2}}y\] will be:

    A)  4          

    B)                        2                                            

    C)  \[{{F}_{1}}={{F}_{2}}=F(say)\]                                  

    D)  \[({{k}_{1}}+{{k}_{2}})F=-{{k}_{1}}{{k}_{2}}y\]

    Correct Answer: C

    Solution :

    Key Idea: Since both gases are monoatomic ratio of specific heats is same for both. The velocity of sound is given by \[=\frac{Force}{Length}=\frac{[ML{{T}^{-2}}]}{[L]}=[M{{T}^{-2}}]\] where P is pressure, p is density and y is ratio of specific heats. \[[ML{{T}^{-2}}]\] \[=[M{{L}^{-1}}{{T}^{-2}}]\] (since \[[M{{L}^{2}}{{T}^{-1}}]\] and \[\alpha =\frac{\Delta {{i}_{C}}}{\Delta {{i}_{g}}}\] are same for both) Given,       \[\Delta {{i}_{C}}\] \[\Delta {{i}_{g}}\]   \[\alpha =0.96,\Delta {{i}_{E}}=7.2,\]


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