[填空题]
The density of a solid sphere is measured wit yx*21i/a7l7 ko pjpqp9(rqmnh p nn s-bgcyp8zb(c:w *,ercentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage ug8w,b nbcpny- csz:* (ncertainty 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 multipld*xawv-gocp*u z)xjrn1,1g r- r) )gwying its volume by the density of the material of dw )r1uw ogn* x-agx)1pj v,rz*r-)gcwhich 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