$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

$A$ body cools in a surrounding which is at a constant temperature of $\theta_0$. Assume that it obeys Newton's law of cooling. Its temperature $\theta$ is plotted against time $t$. Tangents are drawn to the curve at the points $P(\theta = \theta_2)$ and $Q(\theta = \theta_1)$. These tangents meet the time axis at angles of $\varphi_2$ and $\varphi_1$,as shown in the figure.

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

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

In a room where the temperature is $30^{\circ}C$,a body cools from $61^{\circ}C$ to $59^{\circ}C$ in $4$ minutes. The time (in min) taken by the body to cool from $51^{\circ}C$ to $49^{\circ}C$ will be ....... $\text{min}$.

$A$ can is taken out from a refrigerator at $0^{\circ}C$. The atmospheric temperature is $25^{\circ}C$. If $t_1$ is the time taken to heat from $0^{\circ}C$ to $5^{\circ}C$ and $t_2$ is the time taken to heat from $10^{\circ}C$ to $15^{\circ}C$,then: