Two circular discs $A$ and $B$ with equal radii are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves shown in the figure?

The instantaneous temperature difference between a cooling body and its surroundings,which obeys Newton's law of cooling,is $\theta$. Which of the following graphs represents the variation of $\ln \theta$ with time $t$?

$A$ body cools down from $52.5^{\circ} C$ to $47.5^{\circ} C$ in $5 \ min$ and from $47.5^{\circ} C$ to $42.5^{\circ} C$ in $7.5 \ min$. Then,the temperature of the surroundings is (in $^{\circ} C$)

Two metallic spheres $S_1$ and $S_2$ are made of the same material and have identical surface finish. The mass of $S_1$ is three times that of $S_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of $S_1$ to that of $S_2$ is

$A$ cubic metal block of mass $5 \,kg$ and edge length $0.1 \,m$ at an initial temperature of $100^{\circ} C$ is placed on a thermally insulating flat surface and exposed to air at $0^{\circ} C$. The time in seconds required to cool the block to a temperature of $37^{\circ} C$ is closest to. (Note: Specific heat of the metal $= 500 \,J/kg/^{\circ}C$; Heat transfer coefficient from block to air $= 50 \,W/m^2/^{\circ}C$)

$A$ body cools from $50.0^{\circ}C$ to $49.9^{\circ}C$ in $5 \, s$. How long will it take to cool from $40.0^{\circ}C$ to $39.9^{\circ}C$ (in $, s$)? The temperature of the surroundings is $30^{\circ}C$. Assume Newton's Law of Cooling applies.