Let x= [a^2 b^2 c ] be the physical quantity. If the percentage e… - Vidyadip

MCQ

Let $x=\left[\frac{a^2 b^2}{c}\right]$ be the physical quantity. If the percentage error in the measurement of physical quantities $a, b$ and $c$ is 2,3 and 4 percent respectively. Then percentage error in the measurement of $x$ is

A
$7 \%$
✓
$14 \%$
C
$21 \%$
D
$28 \%$

✓

Answer

Correct option: B.

$14 \%$

(b) : Percentage error in $x$ is given by
$
\begin{aligned}
& \frac{\Delta x}{x}=2 \frac{\Delta a}{a}+2 \frac{\Delta b}{b}+\frac{\Delta c}{c} \\
& \frac{\Delta x}{x} \times 100=2 \times 2 \%+2 \times 3 \%+4 \%=14 \%
\end{aligned}
$

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