$A$ liquid in a beaker has temperature $\theta(t)$ at time $t$ and $\theta_0$ is the temperature of the surroundings. According to Newton's law of cooling,the correct graph between $\log_e(\theta - \theta_0)$ and $t$ is:

$A$ very thin metallic shell of radius $r$ is heated to temperature $T$ and then allowed to cool. The rate of cooling of the shell is proportional to ........

$A$ body cools in $7$ minutes from $60^{\circ}C$ to $40^{\circ}C$. What time (in minutes) does it take to cool from $40^{\circ}C$ to $28^{\circ}C$ if the surrounding temperature is $10^{\circ}C$? Assume Newton's Law of cooling holds.

$A$ 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 $69^\circ C$?

There are two spherical balls $A$ and $B$ of the same material with the same surface,but the diameter of $A$ is half that of $B$. If $A$ and $B$ are heated to the same temperature and then allowed to cool,then

$A$ container contains hot water at $100^{\circ}C$. If in time $T_1$ the temperature falls to $80^{\circ}C$ and in time $T_2$ the temperature falls to $60^{\circ}C$ from $80^{\circ}C$,then: