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Q. No.Two rods \(A\) and \(B\) having the same length of \(1\) m are at the same temperature \(30^\circ \text{C}.\) The coefficients of linear expansion of \(A\) and \(B\) are in the ratio \(4:3.\) At what temperature will the length of \(B\) be the same as the length of rod \(A\) at \(180^\circ \text{C}\)?
1.
\(200^\circ \text{C}\)
2.
\(230^\circ \text{C}\)
3.
\(250^\circ \text{C}\)
4.
\(270^\circ \text{C}\)
Subtopic: Thermal Expansion |
78%
Level 2: 60%+
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A \(100\) g of iron nail is hit by a \(1.5\) kg hammer striking at a velocity of \(60\) ms–1. What will be the rise in the temperature of the nail if one-fourth of the energy of the hammer goes into heating the nail?
[Specific heat capacity of iron = \(0.42\) Jg–1 °C–1]
[Specific heat capacity of iron = \(0.42\) Jg–1 °C–1]
| 1. | \(675\)°C | 2. | \(1600\)°C |
| 3. | \(16.07\)°C | 4. | \(6.75\)°C |
Subtopic: Temperature and Heat |
66%
Level 2: 60%+
JEE
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In an experiment to verify Newton’s Law of Cooling, a graph is plotted between the temperature difference \((\Delta T)\) of water and its surroundings and time, as shown in the figure. The initial temperature of the water is \(80^\circ\text C.\) What is the value of \(t_2 \text{?}\)
1. \(12\)
2. \(14\)
3. \(16\)
4. \(18\)
1. \(12\)
2. \(14\)
3. \(16\)
4. \(18\)
Subtopic: Newton's Law of Cooling |
Level 3: 35%-60%
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Given that the coefficient of linear expansion of brass is \(\alpha=0.00002^\circ \text{C}^{-1},\) what rise in temperature is required to increase the length of a brass rod by \(1\text{%} \text{?}\)
1. \(750^\circ \text{C}\)
2. \(500^\circ \text{C}\)
3. \(200^\circ \text{C}\)
4. \(100^\circ \text{C}\)
1. \(750^\circ \text{C}\)
2. \(500^\circ \text{C}\)
3. \(200^\circ \text{C}\)
4. \(100^\circ \text{C}\)
Subtopic: Thermal Expansion |
87%
Level 1: 80%+
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Two rods, one made of copper and the other made of steel, of the same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are \(385~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) and \(50~\text{Js}^{-1}\text{K}^{-1}\text{m}^{-1}\) respectively. The free ends of copper and steel are held at \(100^\circ \text{C}\) and \(0^\circ \text{C}\) respectively. The temperature at the junction is, nearly:
| 1. | \(12^\circ \text{C}\) | 2. | \(50^\circ \text{C}\) |
| 3. | \(73^\circ \text{C}\) | 4. | \(88.5^\circ \text{C}\) |
Subtopic: Conduction |
74%
Level 2: 60%+
NEET - 2022
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The shapes of the black body radiation curves depend on their:
1. Masses
2. Surface areas
3. Materials
4. Temperatures
1. Masses
2. Surface areas
3. Materials
4. Temperatures
Subtopic: Radiation |
63%
Level 2: 60%+
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A pan filled with hot food cools from \(95^\circ \text{C}\) to \(85^\circ \text{C}\) in \(2\) min when the room temperature is \(20^\circ \text{C}.\) The time taken by the food to cool from \(55^\circ \text{C}\) to \(45^\circ \text{C}\) will be:
| 1. | \(260\) s | 2. | \(280\) s |
| 3. | \(300\) s | 4. | \(320\) s |
Subtopic: Newton's Law of Cooling |
80%
Level 1: 80%+
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The pressure that needs to be applied to the ends of a steel wire of length \(20~\text{cm}\) and area of cross-section \(0.5~\text m^2\) to keep its length constant when the temperature is raised by \(200^\circ \text{C}\) is:
(Young's modulus of elasticity \((Y)\) for steel is \(2\times10^{11}\) N/m2 and the coefficient of thermal expansion \((\alpha)\) is \(1.1\times10^{-5}~\text{K}^{-1})\)
(Young's modulus of elasticity \((Y)\) for steel is \(2\times10^{11}\) N/m2 and the coefficient of thermal expansion \((\alpha)\) is \(1.1\times10^{-5}~\text{K}^{-1})\)
| 1. | \(3.2 \times 10^6~\text{Pa}\) | 2. | \(2.2 \times 10^8~\text{Pa}\) |
| 3. | \(4.4 \times 10^8~\text{Pa}\) | 4. | \(2.2 \times 10^9~\text{Pa}\) |
Subtopic: Thermal Stress |
74%
Level 2: 60%+
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The radius of a spherical black body is \(R,\) and \(\alpha\) represents the rate of energy production within the body. The temperature of the given black body in a steady-state is: (where \(\sigma\) is Stefan- Boltzmann constant)
| 1. | \(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)^{\dfrac{1}{4}} \) | 2. | \(\left(\dfrac{\sigma \times 4 \pi R^2}{\alpha}\right)^{\dfrac{1}{4}}\) |
| 3. | \(\left(\dfrac{\alpha}{\sigma \times 4 \pi R^2}\right)\) | 4. | \(\left(\dfrac{4 \pi R^2 \times \sigma}{\alpha}\right)\) |
Subtopic: Stefan-Boltzmann Law |
80%
Level 1: 80%+
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Two bodies \(A\) and \(B\) have emissivities of \(e_{A}\) and \(e_{B}\) respectively. The outer surface areas of two bodies are equal. The two bodies emit total radiant power at the same rate. The ratio of wavelength of \(B\) corresponding to maximum spectral radiancy to that of wavelength of \(A\) corresponding to maximum spectral radiancy is:
| 1. | \(\left(\dfrac{e_B}{e_A}\right)^4\) | 2. | \(\left(\dfrac{e_A}{e_B}\right)^{1\over 2}\) |
| 3. | \(\left(\dfrac{e_B}{e_A}\right)^{1\over 4}\) | 4. | \(\left(\dfrac{e_A}{e_B}\right)^{1\over 4}\) |
Subtopic: Wien's Displacement Law |
57%
Level 3: 35%-60%
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