Equal masses of two liquids are filled in two similar calorimeters. The rate of cooling will

$A$ body cools from $80^{\circ} C$ to $50^{\circ} C$ in $5 \text{ min}$. In the next time of $t \text{ min}$, the body continues to cool from $50^{\circ} C$ to $30^{\circ} C$. The total time taken by the body to cool from $80^{\circ} C$ to $30^{\circ} C$ is
[The temperature of the surroundings is $20^{\circ} C$.] (in $\text{ min}$)

On what does the proportionality constant depend in Newton's law of cooling?

$A$ solid copper cube of edges $1\;cm$ is suspended in an evacuated enclosure. Its temperature is found to fall from $100^{\circ}C$ to $99^{\circ}C$ in $100\;s$. Another solid copper cube of edges $2\;cm$,with similar surface nature,is suspended in a similar manner. The time required for this cube to cool from $100^{\circ}C$ to $99^{\circ}C$ will be approximately ...... $s$.

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

$A$ bucket full of hot 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 relations is correct?