Newton’s law of cooling, holds good only if the temperature difference between the body and the surroundings is

1. Less than 10$°\mathrm{C}$      

2. More than 10$°\mathrm{C}$

3. Less than 100$°\mathrm{C}$     

4. More than 100$°\mathrm{C}$

The temperature of a body falls from \(50^{\circ}\mathrm{C}\)$\mathrm{}$ to \(40^{\circ}\mathrm{C}\)$\mathrm{}$ in 10 minutes. If the temperature of the surroundings is \(20^{\circ}\mathrm{C}\)$\mathrm{,\; t}$hen the temperature of the body after another 10 minutes will be:
1. \(36.6^{\circ}\mathrm{C}\)          
2. \(33.3^{\circ}\mathrm{C}\)$\mathrm{}$
3. \(35^{\circ}\mathrm{C}\)             
4. \(30^{\circ}\mathrm{C}\)$\mathrm{}$

A body takes 5 minutes to cool from 90$°\mathrm{C}$ to 60$°\mathrm{C}$. If the temperature of the surroundings is 20$°\mathrm{C}$, the time taken by it to cool from 60$°\mathrm{C}$ to 30$°\mathrm{C}$ will be. 

1. 5 min                   

2. 8 min

3. 11 min                 

4. 12 min

An object is cooled from 75°C to 65°C in 2 minutes in a room at 30°C. The time taken to cool another object from 55°C to 45°C in the same room in minutes is -

1. 4                   

2. 5

3. 6                   

4. 7

A cane is taken out from a refrigerator at 0°C. The atmospheric temperature is 25°C. If ${\mathrm{t}}_1$ is the time taken to heat from 0°C to 5°C and ${\mathrm{t}}_2$ is the time taken from 10°C to 15°C, then 

1. ${\mathrm{t}}_1>{\mathrm{t}}_2$                         

2. ${\mathrm{t}}_1<{\mathrm{t}}_2$

3. ${\mathrm{t}}_1={\mathrm{t}}_2$                        

4. There is no relation

Two rods (one semi-circular and the other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. Points A and B are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of a straight rod at any given point in time will be:
     
1. 2: $\mathrm{\pi }$ 

2. 1: 2

3. $\mathrm{\pi }$: 2

4. 3: 2

A wall is made up of two layers, A and B. The thickness of the two layers is the same, but the materials are different. The thermal conductivity of A is double that of B. If in thermal equilibrium, the temperature difference between the two ends is \(36^{\circ}\mathrm{C}\)$\mathrm{,\; t}$hen the difference in temperature between the two surfaces of A will be:
1. \(6^{\circ}\mathrm{C}\)$\mathrm{}$

2. \(12^{\circ}\mathrm{C}\)$\mathrm{}$

3. \(18^{\circ}\mathrm{C}\)$\mathrm{}$

4. \(24^{\circ}\mathrm{C}\)$\mathrm{}$

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle ABC , right angled at B. The points A and B are maintained at temperatures T and $\sqrt{2}\mathrm{T}$ respectively. In the steady state the temperature of the point C is ${\mathrm{T}}_{\mathrm{C}}$. Assuming that only heat conduction takes place, $\frac{{\mathrm{T}}_{\mathrm{C}}}{\mathrm{T}}$ is equal to -
1. $\frac{1}{\left(\sqrt{2}+1\right)}$                   

2. $\frac{3}{\left(\sqrt{2}+1\right)}$
3. $\frac{1}{2\left(\sqrt{2}-1\right)}$                  

4. $\frac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

A sphere, a cube and a thin circular plate, all made of the same material and having the same mass are initially heated to a temperature of 1000°C. Which one of these will cool first ?

1. Plate                     

2. Sphere

3. Cube                     

4. None of these

A black metal foil is warmed by radiation from a small sphere at temperature T and at a distance d where surrounding temperature is $T_o$. It is found that the power received by the foil is `P'. If both the temperature and the distance are doubled, the power received by the foil will be- [Assume $T>>T_o$]

1. 16P                 

2. 4P

3. 2P                   

4. P