NEET Sample Paper NEET Sample Test Paper-1

  • question_answer The coefficient of volumetric expansion of mercury is\[1.8\times {{10}^{-5}}^{o}C\]. The thermometer bulb has a velocity of \[{{10}^{-6}}{{m}^{3}}\] and cross-section of stern\[0.002\,c{{m}^{2}}\]. Assuming that bulb is filled with mercury at \[{{0}^{o}}C,\] the length of mercury column at \[{{100}^{o}}C\] will be:

    A)  \[18\,mm\]                  

    B)  \[9\,mm\]

    C)  \[18\,cm\]                   

    D)  \[9\,cm\]

    Correct Answer: B

    Solution :

    Coefficient of volumetric expansion \[(\gamma )\] \[=1.8\times {{10}^{-5}}{{/}^{o}}C\] Initial volume \[V={{10}^{-6}}{{m}^{3}}\] Area of cross section                         \[A=0.02c{{m}^{2}}=2\times {{10}^{-7}}\,c{{m}^{2}}\] Initial temperature \[{{T}_{1}}={{0}^{o}}C\] Final temperature \[{{T}_{2}}={{100}^{o}}C\] The final volume is \[V'=V\left[ 1+\gamma ({{T}_{2}}-{{T}_{1}}) \right]\]                 \[={{10}^{-6}}\,[1+1.8\times {{10}^{-5}}(100-0)]\]                 \[=1.0018\times {{10}^{-6}}\] Change in volume \[\Delta V=A\times \Delta l=V'-V\] (Where \[\Delta l\] is the length of mercury column) \[\Rightarrow \] \[(2\times {{10}^{-7}})\times \Delta l=1.0018\times {{10}^{-6}}-{{10}^{-6}}\] Hence,         \[\Delta l=\frac{0.0018\times {{10}^{-6}}}{2\times {{10}^{-7}}}\]                 \[=0.009m-9\,m\,m\]


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