Kognity IB Physics A.0 Measurements & Uncertainty (id: 5d376f138)

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

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[填空题]
The density of a solid sphere is mea ) woxinw8v:l0sured wh,wr 1-sj kh3xw6g l;eith percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is j6whl31k se- ;wx g,hrthe percentage uncertainty in the mass of the sphere?   % (Please do not include the % simbol in the blank)

参考答案: 20.0


本题详细解析:
The mass of the sphere can be calculated by g5 0x8s /ly8 3isbktmimultiplying its volume by the density of the mater/8i 3mst0l gx5yi bks8ial of which it is made: $$M=\frac{4}{3}\pi r^3\rho$$ so the percentage uncertainty in $M$ is $$\frac{\mathrm{\Delta }M}{M}=3\frac{\mathrm{\Delta }r}{r}+\frac{\mathrm{\Delta }\rho }{\rho }.$$ The percentage uncertainty in $r$ is $5\mathrm{\%}$, so the percentage error in $M$ is $(3\times 5\mathrm{\%})+5\mathrm{\%}=20\mathrm{\%}$

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