[填空题]
The density of a solid sphere is measured with percentage uncerta vz74v vcl *2g ;k0oumyeyzs;-inty of 5%. ps ei8-v 0oev1p3 7encThe radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the masvvon8p s 1i07e-pc 3ees 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 itsh9q(skm*qxrbxaez rm99fx: 5c3. l)f iz +it* volume by the density of the 3l*b rzfes9ra qkf9xx hz:i 9t)c*+ (mqmx5.i 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