[填空题]
The density of a solid sphere znzi1u::j,q sr 0jcu/ is measured with yqjiub-8 t s, , . f8nhed8,xyx9n4mvqpercentage uncertainty of 5%. Theq-y4,8i 8,x9utq njv8d e yxhbmfn., s radius 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 by the dens)lyx*4wvb, q(y6orrut7i 1 3,aujm zvity of the material ofly ma1q,*7rix (yboj 4trvw 6,v3)zu u 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