$A$ body takes $5$ minutes to cool from $90^oC$ to $60^oC$. If the temperature of the surroundings is $20^oC$,the time taken by it to cool from $60^oC$ to $30^oC$ will be ...... $\min.$

The initial temperature of a body is $80^{\circ}C$. If its temperature falls to $64^{\circ}C$ in $5$ minutes and in $10$ minutes to $52^{\circ}C$,then the temperature of the surrounding will be ...... $^{\circ}C$.

$A$ 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 $\text{ sec}$)?

For a system where Newton's law of cooling is applicable,the initial rate of cooling is $R \ ^\circ C/sec$. Find the time when the temperature difference $\Delta T_0$ (initial temperature difference) is reduced to half.

$A$ sphere of density $\rho$,specific heat capacity $c$,and radius $r$ is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of the sphere and is proportional to

$A$ body cools from a temperature of $60^{\circ} C$ to $50^{\circ} C$ in $10 \text{ minutes}$ and $50^{\circ} C$ to $40^{\circ} C$ in $15 \text{ minutes}$. The time taken in minutes for the body to cool from $40^{\circ} C$ to $30^{\circ} C$ is