[填空题]
The density of a solh6j4zp 7 azf;jrm:fk 9id sphere is measured with perce hy/hl 6;s -2lqtskx7nntage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertain7sl;y62/slkn hqh-xt ty 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 cakm m7lyuaa-,d 50z y/hn be calculated by multiplying its volume by the density of the material of whichy-7lkm/ua d0, m5ha zy 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