Two identical conducting rods are first connected independently to two vessels, one containing water at 100$°\mathrm{C}$ and the other containing ice at 0$°\mathrm{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ g / s be the rate of melting of ice in two cases respectively. The ratio of ${\mathrm{q}}_1$/${\mathrm{q}}_2$ is

(a) $\frac{1}{2}$                 (b) $\frac{2}{1}$
(c) $\frac{4}{1}$                 (d) $\frac{1}{4}$

Two metallic spheres \(S_1\) and \(S_2\) are made of the same material and have identical surface finish. The mass of \(S_1\) is three times that of \(S_2\). 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 \(S_1\) to that of \(S_2\) is:
1. \(\dfrac{1}{3}\)
2. \(\left(\dfrac{1}{3}\right)^{1/3}\)
3. \(\dfrac{1}{\sqrt{3}}\)
4. \(\dfrac{\sqrt{3}}{1}\)

Three discs \(A,B\) and \(C\) having radii \(2~\text{m},4~\text{m},\) and \(6~\text{m}\) respectively are coated with carbon black on their surfaces. The wavelengths corresponding to maximum intensity are \(300~\text{nm},400~\text{nm},\) and \(500~\text{nm}\) respectively. The power radiated by them are \(Q_a,Q_b,\) and \(Q_c\) respectively, then:
1. \(Q_a\) is maximum
2. \(Q_b\) is maximum
3. \(Q_c\) is maximum
4. \(Q_a=Q_b=Q_c\)

The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase  from   20$°\mathrm{C}$ to 20.5$°\mathrm{C}$ . If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at 20$°\mathrm{C}$, the temperature of water will be 

1. 21$°\mathrm{C}$               2. 22$°\mathrm{C}$ 
3. 24$°\mathrm{C}$               4. 28$°\mathrm{C}$ 

The energy distribution E with the wavelength $\left(\mathrm{\lambda }\right)$ for the black body radiation at temperature T Kelvin is shown in the figure. As the temperature is increased the maxima will:
     

A hollow copper sphere S and a hollow copper cube C, both of negligible thin walls of same area, are filled with water at 90°C and allowed to cool in the same environment. The graph that correctly represents their cooling is -

In the figure, the distribution of energy density of the radiation emitted by a black body at a given temperature is shown. The possible temperature of the black body is

(1) 1500 K                 

(2) 2000 K

(3) 2500 K                 

(4) 3000 K

The only possibility of heat flow in a thermos flask is through its cork which is 75 ${\mathrm{cm}}^2$ in area and 5 cm thick. Its thermal conductivity is 0.0075 cal/cmsec$°\mathrm{C}$. The outside temperature is 40$°\mathrm{C}$ and latent heat of ice is 80 cal ${\mathrm{g}}^{-1}$. Time taken by 500 g of ice at 0$°\mathrm{C}$ in the flask to melt into water at 0$°\mathrm{C}$ is -

(a) 2.47 hr
(b) 4.27 hr
(c) 7.42 hr
(d) 4.72 hr

Three rods of identical area of cross-section and made from the same metal form the sides of an isosceles triangle ABC, which is 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 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. $\frac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

Two rods (one semi-circular and other straight) of same material and of same cross-sectional area are joined as shown in the figure. The points A and B are maintained at different temperature. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross section of the straight rod in a given time is 

(1) 2 : $\mathrm{\pi }$ 

(2) 1 : 2

(3) $\mathrm{\pi }$ : 2

(4) 3 : 2