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 en$-$or in the measurement of $x$ is

A
$7\%$
✓
$14\%$
C
$21\%$
D
$28\%$

✓

Answer

Correct option: B.

$14\%$

Given: $x=\frac{a^2 b^2}{c}$
Percentage error is given by.
$\frac{\Delta x}{x}=\frac{2 \Delta a}{a}+\frac{2 \Delta b}{b}+\frac{\Delta c}{c}$
$=(2 \times 2)+(2 \times 3)+4$
$=4+6+4=14$
$\therefore \frac{\Delta x }{ x } \%=14 \%$

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