First slide

Accuracy; precision of instruments and errors in measurements

Question

A physical quantity Q is related to four observables x, y, z and t by the relation $Q = \frac{x^{2 / 5} z^{3}}{y \sqrt{t}}$ .The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5%, and 1% respectively. What will be percentage error in Q.

Moderate

Solution

Given relation $Q = \frac{x^{\frac{2}{5}} z^{3}}{y \sqrt{t}}$
$\begin{array}{l} \frac{Δ Q}{Q} = \frac{2}{5} \frac{Δ x}{x} + 3 \frac{Δ z}{z} + \frac{Δ y}{y} + \frac{1}{2} \frac{Δ t}{t} \\ = \frac{2}{5} \times 2.5 + 3 \times 2 + 0.5 + \frac{1}{2} \times 1 \\ = 1 + 6 + 0.5 + 0.5 \\ = 0008.00 \end{array}$

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