[填空题]
The density of a solid sphere:bj /+pj ;lhg /rt4eiu is measured with percentage uncertainty of 5 sy t2fpjgm5dm,:2e8p%. The radiusytf:2jm md2spg pe5 8, 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 multipdi yb0r/ * *ozp5kb3rklying its volume by the density of the materia* r53*b0/ziybrpkd o kl 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