In a room where the temperature is $30^{\circ} C$, a body cools from $61^{\circ} C$ to $59^{\circ} C$ in $4$ minutes. The time taken by the body to cool from $51^{\circ} C$ to $49^{\circ} C$ will be:

$A$ body takes $4$ minutes to cool from $100^{\circ}C$ to $70^{\circ}C$. To cool from $70^{\circ}C$ to $40^{\circ}C$ it will take ........ $\text{min.}$ (room temperature is $15^{\circ}C$)

$A$ body cools from $60^{\circ} C$ to $40^{\circ} C$ in $6$ minutes. After the next $6$ minutes,its temperature will be (Temperature of the surroundings is $10^{\circ} C$). (in $^{\circ} C$)

$A$ pan filled with hot food cools from $94^{\circ}C$ to $86^{\circ}C$ in $2$ minutes. When the room temperature is $20^{\circ}C$, how long will it take to cool from $74^{\circ}C$ to $66^{\circ}C$?

$A$ 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 ........

Two solid spheres of radii $R_1$ and $R_2$ are made of the same material and have similar surfaces. The spheres are raised to the same temperature and then allowed to cool under identical conditions. Assuming the spheres to be perfect conductors of heat,the ratio of their initial rates of cooling is: