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Question: The diameter of a rod is given by d = d<sub>0</sub> (1 + ax) where 'a' is a constant and x is distan...

The diameter of a rod is given by d = d0 (1 + ax) where 'a' is a constant and x is distance from one end. If thermal conductivity of material is K. Then the thermal resistance of the rod if its length is lis –

A

1Kπd02\frac{1}{K\pi d_{0}^{2}}

B

4lKπd02(al+1)\frac{4\mathcal{l}}{K\pi d_{0}^{2}(a\mathcal{l} + 1)}

C

2lKπd02(al+1)2\frac{2\mathcal{l}}{K\pi d_{0}^{2}(a\mathcal{l +}1)^{2}}

D

2lKπd02(al+1)\frac{2\mathcal{l}}{K\pi d_{0}^{2}(a\mathcal{l} + 1)}

Answer

4lKπd02(al+1)\frac{4\mathcal{l}}{K\pi d_{0}^{2}(a\mathcal{l} + 1)}

Explanation

Solution

dR = dxKπd24\frac{dx}{K\frac{\pi d^{2}}{4}} = 4dxKπd02(1+ax)2\frac{4dx}{K\pi d_{0}^{2}(1 + ax)^{2}}

\ R = ∫dR\int_{}^{}{dR}