JEE Main & Advanced Physics Mathematical Tools, Units & Dimensions JEE PYQ - Mathematical Tools Units and Dimensions

  • question_answer
    The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is: [JEE Main Online 08-04-2018]

    A) \[4.5%\]

    B) \[6%\]

    C) \[2.5%\]

    D) \[3.5%\]

    Correct Answer: A

    Solution :

    [a] \[\rho =\frac{m}{{{\ell }^{3}}}\]
    \[\frac{d\rho }{\rho }=\frac{dm}{m}+3\frac{d\ell }{\ell }\]
    \[\frac{d\rho }{\rho }\times 100=\frac{dm}{m}\times 100+3\frac{d\ell }{\ell }\times 100\]
    \[=1.5+3\times 1=4.5%\]


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