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InterviewSolution
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A physcial quantity X is related to four measurable quantites a, b, c and d as follows :`X = a^2 b^3 c^(5//2) d^(-2)` The percentage error in the measurement of a, b, c and d are1% , 2%, 3% and 4%, respectively. What is the percentage error in quantity X ? if the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result ? |
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Answer» Given, physical quantity is `X=a^(2)b^(3)c^(5//2)d^(-2)` Maximum percentage error in X is `(DeltaX)/Xxx100=+-[2((Deltaa)/axx100)+3((Deltab)/bxx100)+5/2((Deltac)/cxx100)+2((Deltad)/d xx100)]` `=+-[2(1)+3(2)+5/2(3)+2(4)]%` `=+-[2+6+15/2+8]=+-23.5%` `therefore" Percentage error in quantity "X=+-23.5%` Mean absolute error in `X=+-0.235=+-0.24` (rounding -off upto significant digits) The calculated value of x should be round-off upto two significant digits. `therefore X=2.8` |
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