[填空题]
The density of a solid)d 58l(efc viuto;hr+z swln v v a81s*;2vxr4dq4xi)474y/vnltso l sphere is measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertain/nqzniv r4yd 4sw71vvl4)s2 tx 4llo;vx*8sa ty 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 muly8sr/o5u arew ,j:qi5tiplying its volume by the density of theq yo sau5/:er8wji,5r 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