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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2002

  • question_answer
    The weight of a metal piece in air is 46 g. When it is immersed in a liquid of relative density 1.24 at \[27{}^\circ C,\]then its weight becomes 30 g. When its temperature increases to\[42{}^\circ ,\]the weight of metal piece becomes 30.5 g. If the relative density of liquid at\[42{}^\circ C\]is 1.2, the coefficient of linear expansion of metal will be

    A)  \[4.3\,\times \,{{10}^{-5}}{{/}^{o}}C\]

    B)  \[2.3\,\times \,{{10}^{-5}}{{/}^{o}}C\]

    C)  \[5.3\,\times \,{{10}^{-5}}{{/}^{o}}C\]

    D)  \[3.4\,\times \,{{10}^{-5}}{{/}^{o}}C\]

    Correct Answer: B

    Solution :

     Weight in air\[=46\text{ }g\] \[30g=46g-{{V}_{D{{\rho }_{27}}g}}\]       ?(i) \[30.5g=46g-{{V}_{D}}'{{\rho }_{42}}g\]  ...(ii) From Eqs. (i) and (ii). \[\frac{V{{'}_{D}}}{{{V}_{D}}}.\frac{{{\rho }_{42}}}{{{\rho }_{27}}}=\frac{15.5}{16}\] \[\frac{{{V}_{D}}(1+\gamma \Delta T)}{{{V}_{D}}}.\frac{1.20}{1.24}=\frac{15.5}{16}(\Delta T=15{}^\circ C)\] \[1+\gamma (15)=\frac{15.5\times 1.24}{1.20\times 16}\] \[\gamma =6.9\times {{10}^{-5}}/{}^\circ C\] Coefficient of linear expansion \[\alpha =\frac{\gamma }{3}=\frac{6.9\times {{10}^{-5}}}{3}=2.3\times {{10}^{-5}}/{}^\circ C\]


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