[填空题]
The density of a solid sphere is measured with percentage unrda ;/w4uif0s7 aeo4 pu2- wtmcertainmqoc xr)5ovx 8.*nsvl. . tec3)6zm jtty of 5%. The radi.)mn tc 5srx3. zlxqe*tcv6 .moj8 ov)us of the 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 7 .)+ /dsravpei00 ujvbk8 agdpg e4b9multiplying its volume by the density of the material of which it is r .u / pbe i+k)vgv p7e0bs9gj8d0daa4made: $$M=\frac{4}{3} \pi r^3 \rho$$ 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