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A cylinder of radius 'R' made of material of coefficient of thermal conductivity $'k_1'$ is surrounded by a cylindrical shell of inner radius 'R' and outer radius 2 R made of a material of coefficient of thermal conductivity $'k_2'$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in the steady state. The effective coefficient of thermal conductivity of the system is :

$\begin {array} {1 1} (1)\;k_1+k_2 & \quad (2)\;\large\frac{k_1+3k_2}{4} \\ (3)\;\large\frac{3k_1+k_2}{4} & \quad (4)\;\large\frac{k_1k_2}{k_1+k_2} \end {array}$

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Ans : (2)
$\large\frac{k_1+3k_2}{4}$
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