Question

A physical quantity $z$, depends upon two other physical quantities $x$ and $y$, as follows. $z=a x^{2} y^{1 / 2}$ where, a is a constant. In an experiment, the quantity $x$ is determined by measuring $z$ and $y$ and using the above expression. If the percentage of error in the measurement of $z$ and $y$ are $10 \%$ and $12 \%$ respectively, then the percentage of error in the determined value of $x$ is

• A. $ 2\% $
• B. $ 8\% $
• C. $ 15\% $
• D. without the value of the constant a, the percentage of error cannot be calculated

Answer 1

Answer: (A)

$z=a x^{2} y^{1 / 2}$
$\frac{\Delta z}{z}=2 \frac{\Delta x}{x}+\frac{1}{2} \frac{\Delta y}{y}$
$\frac{\Delta z}{x} \times 100=\left[2 \frac{\Delta x}{x}+\frac{1}{2} \frac{\Delta y}{y}\right] \times 100$
$10 \%=2 \frac{\Delta x}{x} \times 100+\frac{1}{2} \times 12 \%$
$\frac{\Delta x}{2} \times 100=2 \%$