[填空题]
The density of a solid sphere i a1jt(yq:,dcnrq(y+m s measured:+3b a4sltz2lmd+ppo with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of the sphere?m 3+d +pslpo a24ztl:b % (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 multiplyz, j0ga1k be v,qx6:h(ji u* aoim8v9sing its volume by the density of the material of which it is madebo(vaei gka*61vziq:h9j0,j ,u x8 ms: $$M=\frac{4}{3} \pi r^3 \rho$$ 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 $(3 \times 5 \%)+5 \%=20 \%$
