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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    A physical quantity z, depends upon two other physical quantities x and y, as follows. \[z=a{{x}^{2}}{{y}^{1/2}}\] where, a is a constant. In an experiment, the quantity x is determined by measuring z and y and using the above expression. If the percentage of error in the measurement of z and y are \[10%\] and \[12%\]respectively, then the percentage of error in the determined value of x is

    A)  \[2%\]

    B)  \[8%\]

    C)  \[15%\]

    D)  without the value of the constant a, the percentage of error cannot be calculated

    Correct Answer: A

    Solution :

    \[z=a{{x}^{2}}{{y}^{1/2}}\] \[\frac{\Delta z}{z}=2\frac{\Delta x}{x}+\frac{1}{2}\frac{\Delta y}{y}\] \[\frac{\Delta z}{x}\times 100=\left[ 2\frac{\Delta x}{x}+\frac{1}{2}\frac{\Delta y}{y} \right]\times 100\] \[10%=2\frac{\Delta x}{x}\times 100+\frac{1}{2}\times 12%\] \[\frac{\Delta x}{2}\times 100=2%\]


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