[填空题]
The density of a solid spher)91-ad)j hdi69e t thvgvqro ;e ippf-9bo*mvuz,s8vq/ m k; dk(s measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the perck-b/9*d;,zmp8 kv uq(v mpsfoentage 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 calculatf ql 5l1rygcz 9 tc64ojyy3l1w(uc6/yed by multiplying its volume by the density ofj ycg6z(f96q 5wcu3ro4c1/tly1y yl l 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