[填空题]
The density of a solid s,(c1uy o8egtk- w. yszphere88qkdqr7of l; is measured with percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. Whaq;k f 8q7dol8rt 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 multimnf 5d e;cz,k q1( n:oib5fs*mplying its volume by the density of the material of which it is made m f1kd:i;,b 5qcemf(n*n 5soz: $$M=\frac{4}{3} \pi r^3 \rho$$ 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