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Q. No.The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:
| 1. | \(-40^\circ\) | 2. | \(40^\circ\) |
| 3. | \(0^\circ\) | 4. | \(50^\circ\) |
Subtopic: Temperature and Heat |
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Level 1: 80%+
Hints
The absolute zero temperature on the Fahrenheit scale is (approximately):
1. \(-273^{\circ}\text{F}\)
2. \(-32^{\circ}\text{F}\)
3. \(-460^{\circ}\text{F}\)
4. \(-132^{\circ}\text{F}\)
Subtopic: Temperature and Heat |
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Level 3: 35%-60%
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The graph between two temperature scales \(A\) and \(B\) is shown in the figure. Between upper fixed point and lower fixed point there are \(150\) equal division on scale \(A\) and \(100\) on scale \(B.\) The relationship for conversion between the two scales is given by:
1. \(\dfrac{t_A-180}{100}=\dfrac{t_B}{150} \)
2. \(\dfrac{t_A-30}{150}=\dfrac{t_B}{100} \)
3. \(\dfrac{t_B-180}{150}=\dfrac{t_A}{100} \)
4. \(\dfrac{t_B-40}{100}=\dfrac{t_A}{180}\)
1. \(\dfrac{t_A-180}{100}=\dfrac{t_B}{150} \)
2. \(\dfrac{t_A-30}{150}=\dfrac{t_B}{100} \)
3. \(\dfrac{t_B-180}{150}=\dfrac{t_A}{100} \)
4. \(\dfrac{t_B-40}{100}=\dfrac{t_A}{180}\)
Subtopic: Temperature and Heat |
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Level 2: 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 |
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Level 1: 80%+
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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 |
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Level 2: 60%+
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Two holes are cut into a metal sheet. The diameters of the two holes are \(d_1\) and \(d_2\) \((d_1>d_2).\) If the temperature of the metal sheet is increased, then which of the following distance increases?
| 1. | \(d_1\) | 2. | \(d_2\) |
| 3. | \(AB\) | 4. | All of the above |
Subtopic: Thermal Expansion |
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A hole is drilled in a copper sheet. The diameter of the hole is \(0.5\) cm at \(27^\circ \text{C}.\) The change in diameter of the hole when heated to \(227^\circ \text{C}\) is:
(Coefficient of linear expansion of copper is \(1.70\times10^{-5}\) K–1)
1. \(6.8\times10^{-2}~\text{cm}\)
2. \(6.8\times10^{-3}~\text{cm}\)
3. \(3.4\times10^{-3}~\text{cm}\)
4. \(1.7\times10^{-3}~\text{cm}\)
(Coefficient of linear expansion of copper is \(1.70\times10^{-5}\) K–1)
1. \(6.8\times10^{-2}~\text{cm}\)
2. \(6.8\times10^{-3}~\text{cm}\)
3. \(3.4\times10^{-3}~\text{cm}\)
4. \(1.7\times10^{-3}~\text{cm}\)
Subtopic: Thermal Expansion |
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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 |
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Two rods having coefficient of linear expansion \(\alpha,3\alpha\) are connected end-on-end. The average coefficient of thermal expansion for the composite rod:
| 1. | is \(2\alpha\) |
| 2. | is \(4\alpha\) |
| 3. | can be any value between \(\alpha\) and \(3\alpha\) |
| 4. | can be any value between \(2\alpha\) and \(3\alpha\) |
Subtopic: Thermal Expansion |
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Level 3: 35%-60%
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A circular metallic ring of radius \(R\) has a small gap of width \(d.\) The coefficient of thermal expansion of the metal is \(\alpha\) in appropriate units. If we increase the temperature of the ring by an amount \(\Delta T,\) then the width of the gap:
| 1. | will increase by an amount of \(d\alpha \Delta T\) |
| 2. | will not change |
| 3. | will increase by an amount \(\left ( 2\pi R-d \right )\alpha \Delta T\) |
| 4. | will decrease by an amount of \(d\alpha \Delta T\) |
Subtopic: Thermal Expansion |
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Level 2: 60%+
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