[填空题]
A pyramid has a squao6ltp dh *2xi+udu :*wrei. 8mi0m/teoaqd,u7h8f xfb3 base of side $x$ and height $h$. The volume $V$ of the pyramid is given by the expression: $$V=\frac{x^2 h}{3}$$ If $V$ is measured to $5.0 \%$ and $h$ is measured to $3 \%$, what is the percentage uncertainty of $x ?$ % (Remember to exclude the $\%$ symbol with your answer)
参考答案: 4.0
本题详细解析: As $$ x=\sqrt{\frac{3 V}{h}} $$ then: $$ \frac{\Delta x}{x}=0.5\left(\frac{\Delta V}{V}+\frac{\Delta h}{h}\right) $$ so the percentage uncertainty in $x$ is $0.5 \times(5 \%+3 \%)=4 \%$ Note: you cannot reverse-identify uncertainties, so an answer of 1% (because $3+$ $(2 x)=5)$ is incorrect. You must rearrange the equation first and then propegate the the uncertainties.
Post time 2025-3-14 13:53:00