Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M _{2}$ is $K$ then the thermal conductivity of $M _{1}$ will be ]...............$K$ [Assume steady state heat conduction]
A$10$
B$8$
C$12.5$
D$2$
JEE MAIN 2022, Medium
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B$8$
b $\Delta T \propto R \propto \frac{\ell}{ k }$,
$\frac{\Delta T _{1}}{\Delta T _{2}}=\frac{\ell_{1}}{ k _{1}} \times \frac{ k _{2}}{\ell_{2}}=\frac{16}{ k _{1}} \times \frac{ k }{8}$
$\frac{20}{80}=\frac{16}{ k _{1}} \times \frac{ k }{8} \rightarrow k _{1}=8 k$
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