$A$ metal rod cools at the rate of $4^{\circ}C/min$ when its temperature is $90^{\circ}C$ and at the rate of $1^{\circ}C/min$ when its temperature is $30^{\circ}C$. The temperature of the surrounding is: (in $^{\circ}C$)

$A$ 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 ...... $s$.

$A$ body cools from $60^{\circ} C$ to $40^{\circ} C$ in $6$ minutes. After the next $6$ minutes,its temperature will be (Temperature of the surroundings is $10^{\circ} C$). (in $^{\circ} C$)

$A$ metallic sphere cools from $50^{\circ}C$ to $40^{\circ}C$ in $300 \, s$. If the atmospheric temperature is $20^{\circ}C$,then the sphere's temperature after the next $5$ minutes will be close to $.....^{\circ}C$.

$A$ 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 $= 50 \,W/m^2/^{\circ}C$)

The circuit below is used to heat water kept in a bucket. Assuming heat loss only by Newton's law of cooling, the variation in the temperature of the water in the bucket as a function of time is depicted by