Scientific Skills & Tools (id: 9062e0729)

本题目来源于试卷: Scientific Skills & Tools，类别为 IB物理学

[单选题]
A rectangular prism is obtained by combining two identical cubes as shown in the figure.

The length of one side of a cube is $10.0\pm0.2cm$.

What is the ratio of absolute uncertainty of volume of the rectangular prism to absolute uncertainty of volume of one cube?

A. $\frac{1}{2}$
B. 1
C. 2
D. 5


参考答案:  C


本题详细解析:

For the rectangular prism

$V = l \times w \times h$ where $l = 20.0 \pm 0.4$, $w = 10.0 \pm 0.2$, and $h = 10.0 \pm 0.2$

The uncertainty on the volume is found from adding the fractional uncertainties of the three different dimensions.

$\Delta V=V(\dfrac{\Delta l}{l}+\dfrac{\Delta w}{w}+\dfrac{\Delta h}{h})$

$\Delta V=2000(\dfrac{0.4}{20.0}+\dfrac{0.2}{10.0}+\dfrac{0.2}{10.0})=\pm 120\,cm^3$

For the cube

$V=l^3 \hspace{1em}$ where $l = 10.0 \pm 0.2$

$\Delta V=(V)(3)\dfrac{\Delta l}{l}$

$\Delta V=(1000)(3)(\dfrac{0.2}{10.0})=\pm 60\,cm^3$

Therefore the ratio is $\dfrac{120}{60} = 2$

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