[填空题]
The density of a solid spheregrc6i/ja8 ck3wc e/ +c is measured with percentage uncertainty of 5%. Tt: mqhg zvqt(8h ,nac7f/+bi6he radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mn 6(g mhatc:hz+bq t87i,vf q/ass 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 itskh;sk 6a2ry + tt4-oye7b/u zs volume by the density of the yez4t su6h-t+/kb; 7karso2ymaterial 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