$A$ pan filled with hot food cools from $50^{\circ} C$ to $49.9^{\circ} C$ in $5 \text{ sec}$. How long will it take to cool from $40^{\circ} C$ to $39.9^{\circ} C$, if the room temperature is $30^{\circ} C$ (in $\text{ sec}$)?

Hot water cools from $60^oC$ to $50^oC$ in the first $10$ minutes and to $42^oC$ in the next $10$ minutes. The temperature of the surrounding is ......... $^oC$.

The temperature of a body $\theta$ is slightly more than the temperature of the surrounding $\theta_0$. Its rate of cooling $(R)$ versus the temperature of the body $(\theta)$ is plotted. Its shape would be:

If a metallic sphere cools from $62^{\circ}C$ to $50^{\circ}C$ in $10 \; \text{minutes}$ and in the next $10 \; \text{minutes}$ cools to $42^{\circ}C$,then the temperature of the surroundings is ......... $^{\circ}C$.

$A$ bowl filled with very hot water cools from $98^\circ C$ to $86^\circ C$ in $2$ minutes when the room temperature is $22^\circ C$. How long will it take to cool from $75^\circ C$ to $69^\circ C$?

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