Three rods made of the same material, having the same cross-sectional area but different lengths 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction will be:-

   
1. \(10.8^{\circ}\mathrm{C}\)
2. \(14.6^{\circ}\mathrm{C}\)
3. \(16.4^{\circ}\mathrm{C}\)
4. \(18.2^{\circ}\mathrm{C}\)

\(5 ~\text g\) of water at \(30^{\circ} \text{C}\) and \(5 ~\text g\) of ice at \(-20^{\circ} \text{C}\) are mixed together in a calorimeter. The water equivalent of the calorimeter is negligible, and the specific heat and latent heat of ice are \(0.5~\text{cal/g}^{\circ} \text{C}\) and \(80~\text{cal/g},\) respectively. The final temperature of the mixture is:

Four rods of the same material with different radii \(r\) and the length \(l\) are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1. \(r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}\)
2. \(r =3~\text{cm}, l =9~\text{cm}\)
3. \(r =4~\text{cm}, l =8~\text{cm}\)
4. \(r =1~\text{cm}, l =1~\text{cm}\)

A brass wire \(1.8~\text m\) long at \(27^\circ \text C\) is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of \(-39^\circ \text C,\) what is the tension created in the wire?
( Assume diameter of the wire to be \(2.0~\text{mm}\) , coefficient of linear expansion of brass \(=2.0 \times10^{-5}~\text{K}^{-1},\) Young's modulus of brass\(=0.91 \times10^{11}~\text{Pa}\) )
1. \(3.8 \times 10^3~\text N\) 
2. \(3.8 \times 10^2~\text N\) 
3. \(2.9 \times 10^{-2}~\text N\) 
4. \(2.9 \times 10^{2}~\text N\) 

In an experiment on the specific heat of a metal, a \(0.20~\text{kg}\) block of the metal at \(150^{\circ}\text{C}\) is dropped in a copper calorimeter (of water equivalent of \(0.025~\text{kg}\)) containing \(150~\text{cm}^{3}\) of water at \(27^{\circ}\text{C}.\) The final temperature is \(40^{\circ}\text{C}.\) The specific heat of the metal will be: 
(the heat losses to the surroundings are negligible)
1. \(0 . 40  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
2. \(0 . 43  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
3. \(0 . 54 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
4. \(0 . 61 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

The plots of intensity versus wavelength for three black bodies at temperatures \(T_1,T_2\) and \(T_3\) respectively are as shown. Their temperatures are such that:
           

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. The 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. \(2:\pi\)
2. \(1:2\)
3. \(\pi:2\)
4. \(3:2\)

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

Steam at \(100^{\circ}\mathrm{C}\) is injected into 20 g of \(10^{\circ}\mathrm{C}\) water. When water acquires a temperature of \(80^{\circ}\mathrm{C}\), the mass of water present will be: (Take specific heat of water =1 cal g^-1 \(^\circ\)C^-1 and latent heat of steam = 540 cal g^-1)