[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 $T$ ? % (please only fill in numerical value without the % sign)
参考答案: 4.0
本题详细解析: Remember, square rooting a value halvetrp0oj48 w/n 4qo wvl3s its percentage uncertainty. The percentage uncertainties are therefore combined as fn4 woto/j wl38rv0p4qollows: $$ \frac{\Delta T}{T}=0.5 \times\left(\frac{\Delta l}{l}+\frac{\Delta g}{g}\right) $$ so the percentage uncertainty in $T$ is: $$ 0.5 \times(6 \%+2 \%)=4 \% $$
Post time 2024-8-21 21:38:19