[填空题]
The density of a soligqk2 we rw1g5-d sphere is measured with percentagzd3,wmcf7fdtjxr, 9w )bve3 (e uncertainty of 5%. The radcf3tjw3 bw)r9v d,m,zd7( e fxius of 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 calculated by multiplying its volume b (fku.py p5w(jng)g )yy the density of the materg k.yn)wf(p) 5 u(gypjial 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