Kognity IB Physics A.0 Measurements & Uncertainty (id: d096e644f)

[填空题]
The density of a solid e/:pz, hxycd, sphere is measured with percentagdx5 : xt,rk-vxe uncertainty of 5%. The radius of the sphere is 4.0 ± 0.2 cm. What is the percentage uncertainty in the mass o-d5r v t:x,xxkf 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 mul )b.bdxfx2mdvrz5 )*c 4qvdt 8tiplying its volume by the density of the material o) 5*d2 dq.bmzcvrxf8 )vxd4tb f 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 $(3 \times 5 \%)+5 \%=20 \%$