A quantity Q is formulated as X^ -2 Y^ +3 2 Z^ -2 5 X, Y and Z ar… - Vidyadip

MCQ

A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional errors of 0.1, 0.2 and 0.5 , respectively in measurement. The maximum fractional error of $Q$ is

A
0.1
B
0.8
✓
0.7
D
0.6

✓

Answer

Correct option: C.

0.7

(C) 0.7
Fractional error $=2 \frac{\Delta \mathrm{X}}{\mathrm{X}}+\frac{3}{2} \frac{\Delta \mathrm{Y}}{\mathrm{Y}}+\frac{2}{5} \frac{\Delta \mathrm{Z}}{\mathrm{Z}}$
$=2(0.1)+\frac{3}{2}(0.2)+\frac{2}{5}(0.5)$
$=0.2+0.3+0.2=0.7$

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