A physical quantity X is related to four measurable quantities a, b, c and d as follows: X = a^{2} b^{3} c^{\frac{5}{2}} d^{-2}. The percentage error in the measurement of a, b, c and d are 1%, 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.

Answers (1)

As per the information given in the question, percentage error in a = (\frac{\Delta a}{a})(100) = 1\; ^{o}/_{o}

As per the information given in the question, Percentage error in b = (\frac{\Delta b}{b})(100) = 2\; ^{o}/_{o}

As per the information given in the question, Percentage error in c = (\frac{\Delta c}{c})(100) = 3\; ^{o}/_{o}

As per the information given in the question, Percentage error in d = (\frac{\Delta d}{d})(100) = 4\; ^{o}/_{o}

Percentage error in X = (\frac{\Delta x}{x})(100)

\\\frac{\Delta X}{X}\times 100=\pm(2\times1+3\times2+2.5\times3+2\times4)\\\pm(2+6+7.5+8) =\pm 23.5\; ^{o}/_{o}

Now, let us calculate the mean absolute error

 =\pm \frac{23.5}{100}

=\pm 0.235=0.24 (after rounding up)

Therefore, we get ‘2.8’ after rounding X i.e. 2.763.

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