[填空题]
The density of a solid sphere is 4y-6bsu ve,fd measured with percentage uncertainty of 5%8rsy 9v.mv:u0m pqbl ;. The radius of the sp.9q0m8vvsr;bplym : uhere 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 x(vfsrwc0 9k;by multiplying its volume by the density;xrk s9fw( 0vc of 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