[填空题]
The density of a solid sphere is measured with percentage uu dz9ke :2uienvc 2r.2nceron-;od gi, .rptainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is th;r p- gindo,o.e 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 b,si*cb9i 7 cq)1id :8ylzdv wyy multiplying its volume by the density of the material of whichb9 y:*8i)v lqiiyzdc ,7w sdc1 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