For a small temperature difference between the body and the surroundings,the relation between the rate of loss of heat $R$ and the temperature of the body $\theta$ is depicted by:

Two metallic spheres $P$ and $Q$ are made of the same material and have the same smoothness,but the weight of $P$ is $8$ times that of $Q$. If the two are heated to the same temperature and left to cool,then the ratio of the rate of cooling of $Q$ to that of $P$ is:

$A$ body cools from $80^{\circ} C$ to $50^{\circ} C$ in $5 \text{ min}$. In the next time of $t \text{ min}$, the body continues to cool from $50^{\circ} C$ to $30^{\circ} C$. The total time taken by the body to cool from $80^{\circ} C$ to $30^{\circ} C$ is
[The temperature of the surroundings is $20^{\circ} C$.] (in $\text{ min}$)

Which of the following statements is true/correct?

If a liquid takes $30 \; s$ in cooling from $80^{\circ} C$ to $70^{\circ} C$ and $70 \; s$ in cooling from $60^{\circ} C$ to $50^{\circ} C$,then find the room temperature. (in $^{\circ} C$)

$A$ metallic sphere cools from $50^{\circ}C$ to $40^{\circ}C$ in $300 \, s$. If the atmospheric temperature is $20^{\circ}C$,then the sphere's temperature after the next $5$ minutes will be close to $.....^{\circ}C$.