[填空题]
The density of a solid sphere is measured(i91 *t rydv*pdo 5hdu with perxqns2 v:98dtvt9n * iecentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of th:tt n29v8s *e xd9qvine 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 *pajl+z.,iejbm1 y7c sl 2y/bz;l-vpits volume by the density of the material of which it is may2 v1csp,yb/*j lpzb l ij.aez-l7+m;de: $$M=\frac{4}{3} \pi r^3 \rho$$ 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