[填空题]
The density of a solid sphe, i p426nzghc1k ky4xnre is measured with percentage uncertainty of ;r;o*t ow) f*dlt)ivizc +z )b5%. The radius of the sphere is 4.0 ± 0.2 c*dz;wic+ of)o)vi z;lbr) tt *m. 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 mu)u 3ktstm.y-4 ajcfi +ltiplying its volume by the density ott y3uckf sma 4+.ij)-f the material 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