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 ......... $^oC$.

Two bodies $A$ and $B$ of same mass,area,and surface finish with specific heats $S_A$ and $S_B$ $(S_A > S_B)$ are allowed to cool for a given temperature range. The temperature varies with time as shown in the graphs. Which graph correctly represents the cooling process?

$A$ metal rod cools at the rate of $4^{\circ}C/min$ when its temperature is $90^{\circ}C$ and at the rate of $1^{\circ}C/min$ when its temperature is $30^{\circ}C$. The temperature of the surrounding is: (in $^{\circ}C$)

$A$ 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 $\text{ min}$)

$A$ container is filled with a liquid that cools from $100^{\circ}C$ to $70^{\circ}C$ in $5 \text{ min}$, when kept at a room temperature of $30^{\circ}C$. The time that it must have taken to cool down to $80^{\circ}C$ from its initial temperature is approximately: (in $\text{ min}$)

Two bottles $A$ and $B$ have radii $R_{A}$ and $R_{B}$ and heights $h_{A}$ and $h_{B}$ respectively,with $R_{B}=2 R_{A}$ and $h_{B}=2 h_{A}$. These are filled with hot water at $60^{\circ} C$. Consider that heat loss for the bottles takes place only from side surfaces. If the time the water takes to cool down to $50^{\circ} C$ is $t_{A}$ and $t_{B}$ for bottles $A$ and $B$,respectively,then $t_{A}$ and $t_{B}$ are best related as: