[填空题]
The density of a solidja,9*d4)c ux(/ygyx wxdy3 mk sphere isx b1bi-ye;* us measured with percentage uncertainty of 5%. The radius ofs bx ue*;-b1yi the sphere is 4.0 ± 0.2 cm. What is the 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;8lx x;,9oegkwsq; lp calculated by multiplying its volume by the densitygqok 98xp;;;wx, e lsl of the material of which it is made: $$M=\frac{4}{3} \pi r^3 \rho$$ so the percentage uncertainty in $M$ is $$\frac{\Delta M}{M}=3 \frac{\Delta r}{r}+\frac{\Delta \rho}{\rho} .$$ The percentage uncertainty in $r$ is $5 \%$, so the percentage error in $M$ is $(3 \times 5 \%)+5 \%=20 \%$
Post time 2024-8-21 21:38:19