JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions Question Bank Self Evaluation Test - Physical World, Units and Measurements

  • question_answer
    The resistance R of a wire is given by the relation \[R=\frac{\rho \ell }{\pi {{r}^{2}}}\]. Percentage error in the measurement of \[\rho ,\,\,\ell \] and r is 1%, 2% and 3% respectively. Then the percentage error in the measurement of R is

    A) 6

    B)  9    

    C)  8

    D)  10

    Correct Answer: B

    Solution :

    [b] Given \[R=\frac{\rho \ell }{\pi {{r}^{2}}}\],then \[\frac{\Delta R}{R}\times 100\]              \[=\frac{\Delta \rho }{\rho }\times 100+\frac{\Delta \ell }{\ell }\times 100+2\frac{\Delta r}{r}\times 100\] \[=1%+2%+2\times 3%=9%\]


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