[填空题]
The density of a solid spher33 pli hv2*jwye is measuxud big +u ucw3vo (..ie)/g8+3ed rpghx.b w3red with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 8+w.vbg e+3rudw/p(..uo c ggieb ixxhu3 ) d3cm. 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 calcuv)5 x+k0*l iv hnro8anlated by multiplying its volume by the density of the material of which it is a5n*rv) 8hx +okl0 vnimade: $$M=\frac{4}{3} \pi r^3 \rho$$ 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