[填空题]
The density of a solid sphere is measu 3t ein.i0ckal wiz-(jn4x8 b: j,(thored witt,id 2fbp1o- nuq8 8fyh percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the per, o b8fiytu2-p8d1 fqncentage 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 bevjm0 6ngb(bu/6ic++xcq6 fl f calculated by multiplying its volume by the density of the material ovuqj(gb6cifc6m +0/ bflnx6+ f 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