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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2000

  • question_answer
    \[{{\upsilon }_{1}}\]and\[{{\upsilon }_{2}}\] are the velocities of sound at the same temperature in two monoatomic gases of densities \[{{\rho }_{1}}\]and \[{{\rho }_{2}}\]respectively. If\[{{\rho }_{1}}.{{\rho }_{2}}=\frac{1}{4},\]then the ratio of velocities \[{{\upsilon }_{1}}\]and \[{{\upsilon }_{2}}\]will be:

    A)  \[1:2\]                                 

    B) \[4:1\]

    C)  \[2:1\]                                 

    D)  \[1:4\]

    Correct Answer: C

    Solution :

    Relation for the velocity of sound is \[\upsilon =\sqrt{\gamma \frac{P}{\rho }}\]                 hence \[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}=\sqrt{\frac{{{P}_{1}}}{{{\rho }_{1}}}\times \frac{{{\rho }_{2}}}{{{P}_{2}}}}=\sqrt{\frac{4}{1}}=2:1\]


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