Kognity IB Physics A.0 Measurements & Uncertainty (id: b35d537a9)

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本题目来源于试卷: Kognity IB Physics A.0 Measurements & Uncertainty，类别为 IBDP Physics

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[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 halves its percen1/+0shb:i khp -dnmm4ik 3zmm tage uncertainty. The percentage uncertainties are therefore combiimm 0 b4phsk 3/zimhdk -mn+1:ned as 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: $$ 0.5 \times(6 \%+2 \%)=4 \% $$