[填空题]
The density of a solimq g8) .hb(bd2 e2jbfid sphere is measured withm cfs d3) 16qb8lothv,q 3e,yc 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 spdv3l6qh3c,eq b,o) f1ymsc8there? % (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 gi ;1/i2gie ucx+9de dvolume by the density of the material of which it is madiue d/cg9 1i2ed ;+gixe: $$M=\frac{4}{3} \pi r^3 \rho$$ 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