Q 11-10-120JEE MainJEE Main 2019 (12 Jan, Shift 1)Medium
A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:
Answer: (D) $\dfrac{K_1 + 3K_2}{4}$
Along the length the two parts are in parallel (same length and temperature difference), so conductances add:
$$K\pi(2R)^2 = K_1\pi R^2 + K_2\pi(4R^2 - R^2)$$
$$K = \frac{K_1 + 3K_2}{4}$$
Solution by Sreeraj P, M.Sc Physics