Question

A physical quantity $Q$ is found to depend on observables $x, y$ and $z$ obeying relation $Q =\frac {x^3y^2}{z}$.. The percentage error in the measurements of $x, y$ and $z$ are $1\%, 2\%$ and $4\%$ respectively. What is percentage error in the quantity $Q$ ?

• A. 3%
• B. 1%
• C. 4%
• D. 11%

Answer 1

Answer: (D)

$Q=\frac{x^{3} y^{2}}{z}$ (given)
According to percent error formula
$\frac{\Delta Q}{Q} =3\left|\frac{\Delta x}{x}\right|+2\left|\frac{\Delta y}{y}\right|+\left|\frac{\Delta z}{z}\right|$
where $\frac{\Delta x}{x} =1 \%, \frac{\Delta y}{Y}=2 \%$
and $\frac{\Delta z}{z} =4 \%=3 \times 1 \%+2 \times 2 \%+1 \times 4 \%$
$=3 \%+4 \%+4 \%=11 \%$