[填空题]
The density of a sol dlz/c(3gsq6fvtic+x)k g/.rpc 9yu 5- j g;khfs7 k5vzhmz9+id sphere is measured with 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 sphere? mfgz7kk+-; j5 9szhhv % (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 dqfm4+ yd6 iwyg)psoj,.xwulm 3o2*o.ensity of the material of which it is made:.mw i*ou+q2dp)fl,o w 3xmy4j g s6.oy $$M=\frac{4}{3} \pi r^3 \rho$$ 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