Answer:
(a) L = 149.2 cm
(b) d = 0.033 cm
Explanation:
Note that the resistivity of copper is
[tex]\rho = 1.72\times 10^{-8}~{\rm \Omega . m} = 1.72\times 10^{-6}~{\rm \Omega.cm}[/tex]
and the mass density of copper is
[tex]d = 8.96~{\rm g/cm^3}[/tex]
We will use the following formula to relate the resistance to other parameters
[tex]R = \frac{\rho L}{A} = \frac{\rho L}{\pi r^2}[/tex]
If all the copper with 1.15 g is used, then
[tex]m = dV\\1.15 = 8.96 \times (L\pi r^2)\\L\pi r^2 = 0.128[/tex]
Back to the resistance:
[tex]0.3 = \frac{1.72\times 10^{-6} L}{\pi r^2}\\L = \pi r^2 (1.74\times 10^5)\\L = \frac{0.128}{L}(1.74\times 10^5)\\L = 149.2~{\rm cm}[/tex]
Then, the diameter is
[tex]149.2\times \pi r^2 = 0.128\\r = 0.0165~{\rm cm}\\d = 2r = 0.033~{\rm cm}[/tex]
