[填空题]
The density of a solid sma -a )ohlac9psigi4)g;5g v5phere is measured wit0+hn,afd5au xh percentage uncertainty of 5%. The radius of the sphere is 4.0 ± 0.h5u +, danxfa02 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 itsm xgy /l6c8is9,jbv1c)5f o5/h xc uug volume by the density of the5 c51/,cbyovusm 9uf lx 86cig hxg)/j 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