[填空题]
The density of a solid sphere is mea mzcipd ispu,yg u5j +g,,z645o ja91qhl; .u9z un2ivf0eitq (g 8tqhoo 1 v+10ovf2jsured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of the spv oi1qtteh 02v;ffv .2 (zugoi18+oh0njql9uhere? % (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 mulohrwwu l8 kco6;o.9.ntiplying its volume by the density of the8hc96;. okowr onw u.l 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