[填空题]
The density of a solid/3v;c 6)+y:0nysmj j4 ulrngl 0tmj nf sphere is measured with percentage uncertainty e3stlqesyh s,6ki/k)77 ck geq(xj; 4of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass of the spisg4es 3(q;lj, cshtx7)/kyqk 6k7 eehere? % (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 its volume by the densit+ r17p-a, nioj xt:ge,e qr-mgy of the ma ,me pxt+q7gir -:je agnor-,1terial 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