[填空题]
The density of a solidt5./0n ltz:bonh;;e e8ydcd vj+ak cv:.w1a (phy*fw;0-rtwru6r wg r 3a5 bd sphere is measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.r; f 3h 0p-*5urgrtyb( wraw6w2 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 calcula6b9wxz9z liq 0y 5uu xr3nm*,fted by multiplying its volume by the density of the material o * xmu6xzzbrq5w9u93 n li,y0ff 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