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

  • question_answer
    The density of a sphere is measured by measuring its mass and diameter. If, it is known that the maximum percentage errors in the measurement are 2% and 3%, then find the maximum percentage error in the measurement of density?

    A) 15%

    B)  18% 

    C)  9%

    D)  11%

    Correct Answer: D

    Solution :

    [d] Let m and d be the mass and diameter of the sphere, then the density p of the sphere is given by              \[\rho =\frac{mass}{volume}=\frac{m}{\frac{4}{3}\pi {{\left( \frac{d}{2} \right)}^{3}}}=\frac{6m}{\pi {{d}^{3}}}\] \[or\,{{\left( \frac{d\rho }{\rho }\times 100 \right)}_{\max }}=\left| \frac{dm}{m}\times 100 \right|+\left| \frac{3d(d)}{d}\times 100 \right|\] \[=2+3(3)=11%\]


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