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A physical quantity `rho` is calculated by using the formula `rho =(1)/(10)(xy^(2))/(z^(1//3))`, where x, y and z are experimentally measured quantities. If the fractional error in the measurement of x, y and z are `2%, 1%` and `3%`, respectively, then the maximum fractional error in the calculation of `rho` isA. 0.005B. 0.05C. 0.06D. 0.07 |
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Answer» `epsilon=(xy^(2))/(10z^(1//3))` Take log and differentiate, `(Deltaepsilon)/(epsilon)=(Deltaex)/(x)+(2Deltay)/(y)-(1)/(3)(Deltaz)/(z)` for maximum error, `(Deltaepsilon)/(epsilon)=(Deltax)/(x)+2(Deltay)/(y)+(1)/(3)(Deltaz)/(z)` `=2%+(2xx1%)+((1)/(3)xx3%)` `=2%+2%+1%=5%` |
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