Answer:
Resistance = 3.35*[tex]10^{-4}[/tex] Ω
Explanation:
Since resistance R = ρ[tex]\frac{L}{A}[/tex]
whereas [tex]\rho(x) = a + bx^2[/tex]
resistivity is given for two ends. At the left end resistivity is [tex]2.25* 10^{-8}[/tex] whereas x at the left end will be 0 as distance is zero. Thus
[tex]2.25*10^{-8} = a + b(0)^2\\ 2.25*10^{-8} = a + 0 \\2.25*10^{-8} = a[/tex]
At the right end x will be equal to the length of the rod, so [tex]x = 1.50\\8.50*10^{-8} = (2.25*10^{-8}) + ( b* (1.50)^2 )\\8.50*10^{-8} - (2.25*10^{-8}) = b*2.25\\\frac{6.25*10^{-8}}{2.25} = b\\b = 2.77 *10^{-8}[/tex]
Thus resistance will be R = ρ[tex]\frac{L}{A}[/tex]
where A = π [tex] r^2 [/tex]
so,
[tex]R = \frac{8.50*10^{-8} * 1.50}{3.14*(1.10*10^{-2})^2} \\R=3.35 * 10 ^{-4}[/tex]
