[填空题]
The density of a solid jv4c46-ygkt tsphere is measured with peryv 6p9u4v+ zwl 7vrxq7t tgo78centage uncertainty of 5%. The radius of t vyttwvg+rq746 vxo7 9p87u lzhe sphere 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 by multippng chy1e)elu++o9( q1o4kbplying its volume by the density of thep he1n k9o1u+qybo(lc4 e )gp+ 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 $(3 \times 5 \%)+5 \%=20 \%$
