[填空题]
The density of a solid sph7ec7 h3xgx4km kkr.w.ere is measured with percentage uncbs(k y ca(y 2n5)ssgii(;ifr+ertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of the spher(rb2 is ng (c(ys;)a y+fk5siie? % (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 nznx wg8m .y)tw/;gz 3can be calculated by multiplying its volume by the density omznn /;w gw3y8g)z.txf the material of 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