[填空题]
The density of a solid 8lgle- k fd-,e;+ukai4zn- bhrmh+3esphere is measured with percentage x-rl.fjuk 3d3ll j8.f lti./runcertainty of 5%. The radius of the sphere is 4f./l8dxjilu l3 k .l .fj3r-tr.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 (8 qnzene t9/p/sp 4pfby the density of the material of which it is madee ez4( p/npfpnq9s8t/ : $$M=\frac{4}{3} \pi r^3 \rho$$ 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