$A$ cup of tea cools from $65.5^{\circ} C$ to $62.5^{\circ} C$ in one minute in a room at $22.5^{\circ} C$. How long will it take to cool from $46.5^{\circ} C$ to $40.5^{\circ} C$ in the same room?

Two solid spheres $A$ and $B$ made of the same material have radii $r_A$ and $r_B$ respectively. Both the spheres are cooled from the same temperature under the conditions valid for Newton's law of cooling. The ratio of the rate of change of temperature of $A$ and $B$ is :

The temperature of hot water falls from $60^oC$ to $50^oC$ in $10 \, min$. It takes another $10 \, min$ to fall from $50^oC$ to $42^oC$. Find the temperature of the surroundings in $^oC$.

$A$ body cools from $62^{\circ}C$ to $50^{\circ}C$ in $10$ minutes and to $42^{\circ}C$ in the next $10$ minutes. The temperature of the surrounding is ........ $^{\circ}C$.

Two liquids of equal volume are cooled under identical conditions from $60^{\circ}C$ to $50^{\circ}C$ in $324 \; sec$ and $810 \; sec$ respectively. If the ratio of their specific heats is $3:4$,find the ratio of their densities. (The water equivalent of the calorimeter is negligible.)

Consider two hot bodies $B_1$ and $B_2$ which have temperatures $100^oC$ and $80^oC$ respectively at $t = 0$. The temperature of the surroundings is $40^oC$. The ratio of the respective rates of cooling $R_1$ and $R_2$ of these two bodies at $t = 0$ will be