[填空题]
The density of a solid sphere is meaxr . u5*e ygp84 zi0qofh e+tnxq,f9u*sured with percentage uncertaiqh(y f.nstaro t:rd 1g*9*hh; nty of 5%. The radius of the sphere is 4.0 ± 0.2 cm *:;n ryo qhg 9rhfs.1t(t*hda. 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 sphehu syk2w, 6 z9x f7;-fpe/y qtg-vj*cire can be calculated by multiplying its volume by the density ofz/k;-g, yf6vxytwq-uh ecjfip*7s 2 9 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