A physical quantity
Question:

A physical quantity $z$ depends on four 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 $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and $\mathrm{d} 2 \%, 1.5 \%, 4 \%$ and $2.5 \%$ respectively. The percentage of error in $\mathrm{z}$ is:

1. $12.25 \%$

2. $14.5 \%$

3. $16.5 \%$

4. $13.5 \%$

Correct Option: , 2

Solution:

$\frac{\Delta \mathrm{Z}}{\mathrm{Z}}=\frac{2 \Delta \mathrm{a}}{\mathrm{a}}+\frac{2}{3} \frac{\Delta \mathrm{b}}{\mathrm{b}}+\frac{1}{2} \frac{\Delta \mathrm{c}}{\mathrm{c}}+\frac{3 \Delta \mathrm{d}}{\mathrm{d}}=14.5 \%$