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VMMC VMMC Medical Solved Paper-2015

  • question_answer
    The reading of a barometer on a steel scale is 75 cm, while the room temperature is 30°C. The linear and volumetric expensions for steel and mercury are \[1.2\times {{10}^{-5}}^{o}{{C}^{-1}}\]and \[1.8\times {{10}^{-4}}^{o}{{C}^{-1}}\]\[(\gamma ),\] respectively. The atmospheric pressure can be obtained as

    A) 74.89 cm             

    B)  67.62 cm

    C) 88.67 cm             

    D) 42.70 cm

    Correct Answer: A

    Solution :

    From the formula for the linear expansion, the length at 30°C is given as\[{{l}_{\theta }}=75[1+\alpha (30)]\]...(i) At this temperature suppose the length of mercury column is \[{{l}_{0}}\] while its length at 0°C is \[{{l}_{0}},\] then\[{{l}_{\theta }}={{l}_{0}}\left[ 1+\frac{1}{3}\gamma (30) \right]\]                   ...(ii) From Eqs. (i) and (ii), we get \[{{l}_{0}}\left[ 1+\frac{1}{3}\gamma (30) \right]=75[1+\alpha (30)]\]\[\Rightarrow \]\[{{l}_{0}}=7489cm\]


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