[填空题]
The density of a solid sphere is measured wikies ( jcn 7;/s8hsj5:ao-egjth percentage uncertd:k6pcj..ia(m+d+w f-ym/ky q8 ozho ainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm.kdzf c +.aiy:8- 6 qm /wkh+.pdom(yjo 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 calculated by multiplying its volu.p6cv;pv 8cjes id85g me by the density of the mate6 .eccv d8 ;p8gj5pvisrial 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