Kognity IB Physics A.0 Measurements & Uncertainty (id: 2ed2f71a6)

[填空题]
A pyramid has a squa e 16hw47lb+4vn4jrv2k9 x(h mhjrln o5r c)dx0lcoc*6o+sulz x u+k j57+ crwre 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.