Heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,then the ratio of the amounts of heat conducted through per unit time will be

In an $Ingen-Hauz$ experiment,the wax melts on two rods up to lengths of $10 \ cm$ and $25 \ cm$ respectively. If the two rods are made of different materials,what is the ratio of their thermal conductivities?

Two layers of a wall,$A$ and $B$,are made of different materials. Both layers have the same thickness. For layer $A$,the thermal conductivity is $K_A = 3 K_B$. The total temperature difference across the wall is $20^{\circ}C$. Find the temperature difference across layer $A$ in $^{\circ}C$.

Two metal rods $1$ and $2$ of same lengths have same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$ and cross-sectional areas are $A_1$ and $A_2$,respectively. If the rate of heat conduction in rod $1$ is four times that in rod $2$,then:

Two rods with thermal conductivities $K$ and $3K$ and equal cross-sectional areas are joined as shown in the figure. Their lengths are $1 \ cm$ and $2 \ cm$,respectively. If the temperatures of the two ends of this composite rod are $0^{\circ}C$ and $100^{\circ}C$ (see figure),then the temperature $\phi$ of their interface is:

$Assertion :$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
$Reason :$ The thermal conductivity of brass is more than the thermal conductivity of wood.