Two metallic blocks $M_{1}$ and $M_{2}$ of the same cross-sectional area are connected to each other as shown in the figure. If the thermal conductivity of $M_{2}$ is $K$,then the thermal conductivity of $M_{1}$ will be $xK$. Find the value of $x$. [Assume steady-state heat conduction]

$A$ rod $A$ of length $40\, cm$ has a temperature difference of $80^\circ C$ at its two ends. Another rod $B$ of length $60\, cm$ has a temperature difference of $90^\circ C$ at its ends. Both rods have the same area of cross-section. If the rate of flow of heat is the same for both,then the ratio of their thermal conductivities $(K_A : K_B)$ will be:

An aluminium rod of length $1 \,m$ and a steel rod of length $2 \,m$, both having the same cross-sectional area, are soldered together end-to-end. The thermal conductivity of the aluminium rod and the steel rod is $200 \,Js^{-1} \,m^{-1} \,K^{-1}$ and $50 \,Js^{-1} \,m^{-1} \,K^{-1}$ respectively. The temperatures of the free ends are maintained at $300 \,K$ and $500 \,K$. What is the temperature of the junction (in $\,K$)?

For cooking the food,which of the following type of utensil is most suitable?

If the ratio of the coefficient of thermal conductivity of silver and copper is $10 : 9$,then the ratio of the lengths up to which wax will melt in the Ingen Hausz experiment will be:

$A$ copper rod of length $10 \ cm$ and cross-sectional area $100 \ cm^2$ is to conduct $4000 \ J/s$ of heat. The thermal conductivity of copper is $400 \ W/m \cdot ^\circ C$. The temperature difference between the two ends of the rod must be maintained at ............. $^\circ C$.