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EAMCET Medical EAMCET Medical Solved Paper-2009

  • question_answer
    The volume of mercury in the bulb of a thermometer is \[{{10}^{-6}}{{m}^{3}}\]. The area of cross- section of the capillary tube is \[2\times {{10}^{-7}}{{m}^{2}}.\]If the temperature is raised by \[100{}^\circ C\], the increase in the length of the mercury column is \[\left( {{\gamma }_{Hg}}=18\,\times \,{{10}^{-5}}{{/}^{0}}C \right)\]

    A)  18 cm                                  

    B)  0.9 cm

    C)   9 cm                                    

    D)  1.8 cm

    Correct Answer: C

    Solution :

     By cubical expansion relation. \[\Delta V=V\times \gamma \times \Delta T\]where \[\gamma \] is coefficient of cubical expansion and \[V={{10}^{-6}}{{m}^{3}}=\]initial volume \[\gamma =18\times {{10}^{-5}}/{{\,}^{o}}C\] \[\Delta T=100{{\,}^{o}}C\]                 \[\therefore \]  \[\Delta V={{10}^{-6}}\times 18\times {{10}^{-5}}\times {{10}^{2}}\]                                 \[=18\times {{10}^{-9}}\]                 Since,                    \[\Delta V=A\times \Delta l\]                 \[\therefore \]  \[18\times {{10}^{-9}}=2\times {{10}^{-7}}\times \Delta l\]                 or            \[9\times {{10}^{-2}}=\Delta l\]                 or            \[\Delta l=9\,cm\]


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