[填空题]
The density of a solid sphere is measured with :suhzwnd*) 0o);bujv per 8zfwvmtv4bs12-aw:z centage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in tmvb 4tvs 1za82zfw-w :he 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*7u neblv2+ pnoiohnlq9;ta 75iy77y be calculated by multiplying its volume by the density l5ei v 7o7an7 pytuh+n;2l9qn7ib o *yof 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