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# Two metal rods have their thermal conductivities $\;K_{1}\;$ and $\;K_{2}\;$ in the ratio 3 : 2 so that their thermal resistance are the same . Then their lengths are is the ratio ( Area of C .S . are the same )

$(a)\;9 : 4\qquad(b)\;3 : 2\qquad(c)\;2 : 3\qquad(d)\;1 : 1$

Answer : $3 : 2$
Thermal resistance = $\;\large\frac{L}{KA}$
$\large\frac{L_{1}}{K_{1}A_{1}}=\large\frac{L_{2}}{K_{2}A}$
$\large\frac{L_{1}}{L_{2}}=\large\frac{K_{1}}{K_{2}}$
$= 3 : 2$