[填空题]
The density of a sol e*grf9an l5;kid spheruw 9d-r:wu ,9 6s;l3jnqbb acj*ms*t 5h.uiube is measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage un.hwqcs3*,5r db aw6u9ulb 9*btsj :iunumj-;certainty 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 multiplying its volume by the densnss7li at16 k(ityi (las 1n6kst7 of 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