According to Newton's law of cooling,the rate of cooling of a body is proportional to $(\Delta \theta )^n$,where $\Delta \theta$ is the difference of the temperature of the body and the surroundings,and $n$ is equal to

$A$ hot body is allowed to cool. The surrounding temperature is constant at $30^{\circ} C$. It takes time $t_{1}$ to cool from $70^{\circ} C$ to $68^{\circ} C$ and time $t_{2}$ to cool from $60^{\circ} C$ to $59.5^{\circ} C$. Then:

The temperature of an iron block falls from $100 \, ^\circ\text{C}$ to $90 \, ^\circ\text{C}$ in time $t_1$,from $90 \, ^\circ\text{C}$ to $80 \, ^\circ\text{C}$ in time $t_2$,and from $80 \, ^\circ\text{C}$ to $70 \, ^\circ\text{C}$ in time $t_3$. Then:

Two spheres of the same metal have radii $r$ and $2r$. They are heated to the same temperature and placed in the same environment. The ratio of their rates of cooling will be:

$A$ body takes $10 \, \text{minutes}$ to cool from $60 \, ^\circ\text{C}$ to $50 \, ^\circ\text{C}$. The temperature of the surroundings is constant at $25 \, ^\circ\text{C}$. Then, the temperature of the body after the next $10 \, \text{minutes}$ will be approximately ....... $^\circ\text{C}$

$A$ cubic metal block of mass $5 \,kg$ and edge length $0.1 \,m$ at an initial temperature of $100^{\circ} C$ is placed on a thermally insulating flat surface and exposed to air at $0^{\circ} C$. The time in seconds required to cool the block to a temperature of $37^{\circ} C$ is closest to. (Note: Specific heat of the metal $= 500 \,J/kg/^{\circ}C$; Heat transfer coefficient from block to air $= 50 \,W/m^2/^{\circ}C$)