[填空题]
The density of a solid z3mw13p 6)g tz;aowaisphere is me3 j(szkoh6r*ax 0c:ds *y9cisohn+-t asured with percentage uncertainty of 5%. The radius of aho+s0c*- d 6cin:3y zosk9sx(jrh *tthe 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 multiplying its volume by the den2onmt;a7q8 nq sity of the material of which it is madean28m7t qoq n;: $$M=\frac{4}{3} \pi r^3 \rho$$ 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