According to $Newton's$ $Law$ $of$ $cooling$,the rate of cooling of a body is proportional to the

$A$ sphere having temperature $600 \text{ K}$ is losing heat due to radiation. At this temperature its rate of cooling is $R$. The rate of cooling of this sphere at $400 \text{ K}$ is $\frac{x}{243}R$. The value of $x$ is (Temperature of surrounding is $300 \text{ K}$)

$A$ 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?

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 ....... $\text{min}$.

An object cools from $100^{\circ} C$ to $40^{\circ} C$ in $10$ minutes, when the surrounding temperature is $10^{\circ} C$. Then the time taken by the object to cool from $70^{\circ} C$ to $20^{\circ} C$ is
$ [\text{Take } \ln 2=0.7, \ln 3=1.1, \ln 6=1.8 ]$ (in $min$)

$A$ sphere of density $\rho$,specific heat capacity $c$,and radius $r$ is hung by a thermally insulating thread in an enclosure which is kept at a lower temperature than the sphere. The temperature of the sphere starts to drop at a rate which depends upon the temperature difference between the sphere and the enclosure and the nature of the surface of the sphere and is proportional to