$A$ metal sphere cools at a rate of $1.5^{\circ} C / min$ when its temperature is $80^{\circ} C$. When the temperature of the sphere is $40^{\circ} C$,its rate of cooling is $0.3^{\circ} C / min$. The temperature of the surrounding $\left(\theta_0\right)$ is (in $^{\circ} C$)

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:

Two identical beakers $A$ and $B$ contain equal volumes of two different liquids at $60\,^oC$ each and are left to cool down. The liquid in $A$ has a density of $8 \times 10^2\, kg/m^3$ and a specific heat of $2000\, Jkg^{-1}K^{-1}$,while the liquid in $B$ has a density of $10^3\, kg/m^3$ and a specific heat of $4000\, Jkg^{-1}K^{-1}$. Which of the following best describes their temperature versus time graph schematically? (Assume the emissivity of both the beakers to be the same.)

If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$,the graph between the temperature $T$ of the metal and time $t$ will be closest to:

Newton's law of cooling is based upon which of the following principles?

$A$ solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120^{\circ}C$,then