A body cools from $62\,^oC$ to $50\,^oC$ in $10\, minutes$ and to $42\,^oC$ in the next $10\, minutes$. The temperature of the surrounding is …….. $^oC$

Two rods $A$ and $B$ of same cross-sectional are $A$ and length $l$ connected in series between a source $(T_1 = 100^o C)$ and a sink $(T_2 = 0^o C)$ as shown in figure. The rod is laterally insulated The ratio of the thermal resistance of the rod is 

Two spheres of the same material have radii $1\ m$ and $4\ m$ and temperatures $4000\ K$ and $2000\ K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

A cylinder of radius $R$ made of a material of thermal conductivity $K_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity $K_2$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

A body cools in a surrounding which is at a constant temperature of $\theta _0$ . Assuming that it obeys Newton's law of cooling, its temperature $\theta $ is plotted against time $t$ . Tangents are drawn to the curve at the points $A(\theta  = \theta _1)$ and $B(\theta = \theta _2)$ . These tangents meet the time-axis at angles $\alpha _1$ and $\alpha _2$ as shown in the graph then