A physical quantity A is dependent on other four physical quantit… - Vidyadip

MCQ

A physical quantity $A$ is dependent on other four physical quantities $p, q, r$ and $s$ as given below $A=\frac{\sqrt{pq}}{r^2s^3} .$ The percentage error of measurement in $p, q, r$ and $s$ $1\%,$ $3\%,\,\, 0.5\%$ and $0.33\%$ respectively, then the maximum percentage error in $A$ is .......... $\%$

A
$2$
B
$0$
✓
$4$
D
$3$

✓

Answer

Correct option: C.

$4$

c
$\frac{\Delta \mathrm{A}}{\mathrm{A}}=\frac{1}{2} \frac{\Delta \mathrm{P}}{\mathrm{P}}+\frac{1}{2} \frac{\Delta \mathrm{q}}{\mathrm{q}}+\frac{2 \Delta \mathrm{r}}{\mathrm{r}}+3 \frac{\Delta \mathrm{s}}{\mathrm{s}}$

$=0.5+1.5+1+1=4 \%$

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