Q. No.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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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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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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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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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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A metallic rod of length \(l\) (at \(0^\circ\text C\)) expands by \(\Delta l\) when its temperature is increased by \(100^\circ\text C.\) This rod is kept on a surface with its left end maintained at \(0^\circ\text C,\) and its right end at \(100^\circ\text C.\) The rod is insulated along its length, so heat can only be exchanged at the ends. The length of the rod is:
| 1. | \(l+\Delta l\) | 2. | \(l+\dfrac{\Delta l}{2}\) |
| 3. | \(l+\dfrac{\Delta l}{4}\) | 4. | \(l+\dfrac{3\Delta l}{4}\) |
Subtopic: Thermal Expansion |
Level 3: 35%-60%
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A steel tape \(1\) m long is correctly calibrated for a temperature of \(27^\circ \text{C}\). The length of a steel rod measured by this tape is found to be \(63.0\) cm on a hot day when the temperature is \(45^\circ \text{C}\). What is the actual length of the steel rod on that day?
(Coefficient of linear expansion of steel = \(1.20\times 10^{-5}~\text{K}^{-1}\)).
1. \( 62.485 \) cm
2. \( 60.762 \) cm
3. \( 65.935 \) cm
4. \( 63.013\) cm
Subtopic: Thermal Expansion |
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As the temperature is increased, the period of a pendulum:
| 1. | increases as its effective length increases even though its centre of mass still remains at the centre of the bob. |
| 2. | decreases as its effective length increases even though its centre of mass still remains at the centre of the bob. |
| 3. | increases as its effective length increases due to the shifting of the centre of mass below the centre of the bob. |
| 4. | decreases as its effective length remains the same but the centre of mass shifts above the centre of the bob. |
Subtopic: Thermal Expansion |
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Level 2: 60%+
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A bimetallic strip is made of aluminium and steel \(\left(\alpha_{A l}>\alpha_{\text {steet }}\right)\). On heating, the strip will:
| 1. | remain straight. |
| 2. | get twisted. |
| 3. | will bend with aluminium on the concave side. |
| 4. | will bend with steel on the concave side. |
Subtopic: Thermal Expansion |
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