Q. No.A spherical black body with a radius of \(12\) cm radiates \(450\)-watt power at \(500\) K. If the radius were halved and the temperature doubled, the power radiated in watts would be:
1. \(225\)
2. \(450\)
3. \(1000\)
4. \(1800\)
A piece of ice falls from a height \(h\) so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice, and all energy of ice gets converted into heat during its fall. The value of \(h\) is: (Latent heat of ice is \(3.4\times10^5\) J/kg and \(g=10\) N/kg)
| 1. | \(544\) km | 2. | \(136\) km |
| 3. | \(68\) km | 4. | \(34\) km |
Two rods \(A\) and \(B\) of different materials are welded together as shown in the figure. Their thermal conductivities are \(K_1\) and \(K_2.\) The thermal conductivity of the composite rod will be:
| 1. | \(\frac{3(K_1+K_2)}{2}\) | 2. | \(K_1+K_2\) |
| 3. | \(2(K_1+K_2)\) | 4. | \(\frac{(K_1+K_2)}{2}\) |
The power radiated by a black body is \(P\) and it radiates maximum energy at wavelength \(\lambda_0.\)
| 1. | \( \dfrac{3}{4} \) | 2. | \( \dfrac{4}{3} \) |
| 3. | \( \dfrac{256}{81} \) | 4. | \( \dfrac{81}{256}\) |
Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at \(100~^{\circ}\text{C},\) while the other one is at \(0~^{\circ}\text{C}.\) If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is:
| 1. | \(50~^{\circ}\text{C}\) |
| 2. | more than \(50~^{\circ}\text{C}\) |
| 3. | less than \(50~^{\circ}\text{C}\) but greater than \(0~^{\circ}\text{C}\) |
| 4. | \(0~^{\circ}\text{C}\) |
A body cools from a temperature of \(3T\) to \(2T\) in \(10\) minutes. The room temperature is \(T.\) Assuming that Newton's law of cooling is applicable, the temperature of the body at the end of the next \(10\) minutes will be:
| 1. | \(\frac{7}{4}T\) | 2. | \(\frac{3}{2}T\) |
| 3. | \(\frac{4}{3}T\) | 4. | \(T\) |
The coefficient of linear expansion of brass and steel rods are \(\alpha_1\) and \(\alpha_2\). Lengths of brass and steel rods are \(L_1\) and \(L_2\) respectively. If \((L_2-L_1)\) remains the same at all temperatures, which one of the following relations holds good?
1. \(\alpha_1L_2^2=\alpha_2L_1^2\)
2. \(\alpha_1^2L_2=\alpha_2^2L_1\)
3. \(\alpha_1L_1=\alpha_2L_2\)
4. \(\alpha_1L_2=\alpha_2L_1\)
1. \({U}_3 =0 \)
2. \({U}_1 >{U}_2 \)
3. \({U}_2 >{U}_1 \)
4. \({U}_1 =0\)
[Latent heat of ice is \(3.4 \times 10^5~\text{J/kg}\) and \(g=10~\text{N/kg}\)]
1. \(544~\text{km}\)
2. \(136~\text{km}\)
3. \(68~\text{km}\)
4. \(34~\text{km}\)
The value of the coefficient of volume expansion of glycerine is \(5\times10^{-4}~\text{K}^{-1}.\) The fractional change in the density of glycerine for a rise of \(40^\circ \text{C}\) in its temperature is:
| 1. | \(0.015\) | 2. | \(0.020\) |
| 3. | \(0.025\) | 4. | \(0.010\) |
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