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

Two metallic spheres ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are made of the same material and have identical surface finish. The mass of ${\mathrm{S}}_1$ is three times that of ${\mathrm{S}}_2$. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of the initial rate of cooling of ${\mathrm{S}}_1$ to that of ${\mathrm{S}}_2$ is 

1. $1/3$             

2. ${\left(1/3\right)}^{1/3}$

3. $1/\sqrt{3}$          

4. $\sqrt{3}/1$