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

A body cools in $7$ minutes from ${60^o}C$ to ${40^o}C$ What time (in minutes) does it take to cool from ${40^o}C$ to ${28^o}C$ if the surrounding temperature is ${10^o}C$? Assume Newton’s Law of cooling holds

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 $P(\theta = {\theta _1})$ and $Q(\theta = {\theta _2})$. These tangents meet the time axis at angles of ${\varphi _2}$and ${\varphi _1}$, as shown

A liquid in a beaker has temperature $\theta (t)$ at time $t$ and $\theta_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between loge $log_e(\theta – \theta_0) $ and $t$ is

A solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $T$, then