Question

A physical quantity $z$ depends on fout observables $a , b , c$ and $d$, as $z =\frac{ a ^{2} b ^{\frac{2}{3}}}{\sqrt{ c } d ^{3}}$ The percentage of error in the measurement of $a, b, c$ and $d$ $2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $z$ is:

• A. $12.25 \%$
• B. $14.5 \%$
• C. $16.5 \%$
• D. $13.5 \%$

Answer 1

Answer: (B)

Given: $z=\frac{a^2 b^{2 / 3}}{\sqrt{c} d^3}$
Percentage error in Z,
$\frac{\Delta Z}{Z}=\frac{2 \Delta a}{a}+\frac{2 \Delta b}{3 b}+\frac{1 \Delta c}{2 c}+\frac{3 \Delta d}{d} $
$=2 \times 2+\frac{2}{3} \times 1.5+\frac{1}{2} \times 4+3 \times 2.5=14.5 \%$