[填空题]
The density of a solid sphere is measured with percentage uncertainty of 0bcx+aaa2rz/5%. llw/0.t,yvdeb8: 8/ylgb ee-dkisf6 The radius of the sphere is 4.0 ,ebld/6dy8ik8fs be g0.ytl v/e wl: -± 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 cg0r ze nvw28iky7 1o:lalculated by multiplying its volume by the density:8knzwove y r027lg 1i of 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