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JIPMER Jipmer Medical Solved Paper-2005

  • question_answer
    A steel scale measures the length of a copper wire as 80.0 cm, when both are at \[20{}^\circ C,\] the calibration temperature for the scale. What would the scale read for the length of the rod when both are at\[40{}^\circ C\]. Given: a for steel \[=11\times {{10}^{-6}}\text{per }{}^\circ C\]and a for\[Cu=17\times {{10}^{-6}}\text{per}\,{}^\circ C\]

    A)  80.0096 cm

    B)                         80.0272 cm        

    C)         1 cm                     

    D)         25.2 cm

    Correct Answer: A

    Solution :

    Using the relation \[{{l}_{t}}={{l}_{0}}(1+\alpha t)\]    \[=1\times [1+11\times {{10}^{-6}}\times (40{}^\circ -20{}^\circ )]\]    \[=1.00022\,cm\] Now length of copper rod at \[40{}^\circ C\] \[R_{t}^{}={{l}_{0}}^{}(1+\alpha t)\] \[=80\,[1+17\times {{10}^{-6}}(40{}^\circ -20{}^\circ )]=80.0272\,cm\] Now number of \[cms\] observed on the scale \[=\frac{80.0272}{1.00022}=80.0096\]


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