[填空题]
The density of a soli3hsem xg o7c .e-+kcg(d sphere is measured with perce)vgz9rq6 *+dowrq;m5r /vdgjntage uncertainty of 5%. The radius+; )vdq5gq vz/orgw jmrr* 9d6 of the sphere is 4.0 ± 0.2 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 calculated by muls 5 wjqlfj)hz0pg lbrs r.ay6cvw -4k,zr5* 88tiplying its volume by the density of the material of which it is )za5*s6rzl-5 0kg pj8ywf4r hwb qscv.,8 rljmade: $$M=\frac{4}{3} \pi r^3 \rho$$ 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