[填空题]
The density of a solid sph69v+ bajjeva-ere is measured with pf aazcm +xlg:uj3 3dno1ycsf8 4*pg9/ercentage uncertainty of 5%. The radius of th3f o43mgulpd1:/x f*yacsc+9jzn ag8e 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 multiplying it+h;* thj byd8qs volume by the density of the material of which it is made+b8;*jtqh hyd : $$M=\frac{4}{3} \pi r^3 \rho$$ 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