[填空题]
The period $T$ of oscillation of a pendulum of length $l$ is given by: $$T=2 \pi \sqrt{\frac{l}{g}} .$$ If the uncertainty in $g$ is $2.0 \%$ and the uncertainty in $l$ is $6.0 \%$, what is the percentage uncertainty in $T$ ? % (only fill in numerical value without the % sign and keep two significant figures)
参考答案: 4.0
本题详细解析: Remember, square rooting a value halves its percentan5r 0y/n s4askge uncertainty. The percentage uncertainties are therefore combined an/r ks0nasy 45s follows: $$ \frac{\Delta T}{T}=0.5 \times\left(\frac{\Delta l}{l}+\frac{\Delta g}{g}\right) $$ so the percentage uncertainty in $T$ is: $$ 0.5 \times(6 \%+2 \%)=4 \% $$
Post time 2024-8-21 21:38:19