[填空题]
The density of a soli8,c mfkhj;b.84 sgwm m25 zuhpd sphere is measured a t1 ehx:q7vih0k3kvl((j8ac with percentage uncertainty of 5%. The radius of c jvxak et 7a:ih3hv(0k(81qlthe 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;(qh91 7hfthc hwp9v5 grqbz b)9pa/ v can be calculated by multiplying its volume by the density of the materhfbqap vg z ch1/w97h59)q(btp ;9hr vial 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