[填空题]
The density of a sollm ms3qewq(2 ; +n6 wyv*fb3r5rua7pf xdm4c5go5aw pvu/v 74g 6 fd1lid sphere is measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the pu/dpdo gv56 4l1 x gc4wvma57fercentage 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 bsceriipr2 fgf35 m40d zqd.+2p)9foge calculated by multiplying its volume by the density of the materfggi 4c0ef3spri)5mr dz+ o.922fd pqial 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