$A$ 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

If a liquid cools from $95^{\circ}C$ to $90^{\circ}C$ in $30 \, s$ and from $55^{\circ}C$ to $50^{\circ}C$ in $70 \, s$,then the temperature of the surroundings is ...... $^{\circ}C$. (in $.5$)

One day in the morning,Ramesh filled up $\frac{1}{3}$ of a bucket with hot water from a geyser to take a bath. The remaining $\frac{2}{3}$ was to be filled with cold water (at room temperature) to bring the mixture to a comfortable temperature. Suddenly,Ramesh had to attend to some work that would take $5-10 \text{ min}$ before he could take a bath. He had two options: $(1)$ fill the remaining bucket completely with cold water and then attend to the work,$(2)$ first attend to the work and then fill the remaining bucket just before taking a bath. Which option do you think would have kept the water warmer? Explain.

$A$ bucket full of water cools from $75^{\circ}C$ to $70^{\circ}C$ in time $T_1$,from $70^{\circ}C$ to $65^{\circ}C$ in time $T_2$,and from $65^{\circ}C$ to $60^{\circ}C$ in time $T_3$. Which of the following is correct?

Assuming Newton's law of cooling to be valid,a body at temperature $50^{\circ} C$ in a surrounding of temperature $20^{\circ} C$ achieves a steady state with the help of a $100 \ W$ heater. If the same body has a temperature of $35^{\circ} C$ in the same surrounding,then the power of the heater required to maintain a steady state is ........ $W$.

$A$ cup of tea cools from $80\,^{\circ}C$ to $60\,^{\circ}C$ in $1\,min$. The ambient temperature is $30\,^{\circ}C$. In cooling from $60\,^{\circ}C$ to $50\,^{\circ}C$,it will take ....... $sec$.