Q129 / 150 · MHT CET 2026 (15 April Shift 2) · Physics
The ratio of the thermal conductivity of two rods of different materials is 6:5. The two rods of same area of cross section and same thermal resistance will have the length in the ratio
- A$5 : 6$
- Correct answerB$6 : 5$
- C$1 : 3$
- D$3 : 1$
Solution
Thermal resistance of a rod is given by $R = \dfrac{L}{KA}$
Given that both rods have the same thermal resistance ($R_1 = R_2$) and the same area of cross-section ($A_1 = A_2 = A$), we can write:
$\dfrac{L_1}{K_1 A} = \dfrac{L_2}{K_2 A}$
$\dfrac{L_1}{L_2} = \dfrac{K_1}{K_2}$
The ratio of thermal conductivities is given as $\dfrac{K_1}{K_2} = \dfrac{6}{5}$
Therefore, $\dfrac{L_1}{L_2} = \dfrac{6}{5}$
The lengths of the rods are in the ratio $6 : 5$.
Given that both rods have the same thermal resistance ($R_1 = R_2$) and the same area of cross-section ($A_1 = A_2 = A$), we can write:
$\dfrac{L_1}{K_1 A} = \dfrac{L_2}{K_2 A}$
$\dfrac{L_1}{L_2} = \dfrac{K_1}{K_2}$
The ratio of thermal conductivities is given as $\dfrac{K_1}{K_2} = \dfrac{6}{5}$
Therefore, $\dfrac{L_1}{L_2} = \dfrac{6}{5}$
The lengths of the rods are in the ratio $6 : 5$.
Hence, the correct answer is option: 'B'.