Q. No.The temperature of a metal strip having coefficient of linear expression \(\alpha\) is increased from \(T_1\) to \(T_2\) resulting in increase of its length by \(\Delta{L_1}.\) The temperature is further increased from \(T_2\) to \(T_3\) such that the increase in its length is \(\Delta{L}_2.\)
Given \(T_3+T_1 =2T_2\) and \(T_2-T_1=\Delta{T},\) the value of \(\Delta{L}_2\) is:
1. \(\Delta{L_1}[1+ 2\alpha^{2}(\Delta{T})^{2}]\)
2. \(\Delta{L_1}[1+ \alpha^{2}(\Delta{T})^{2}]\)
3. \(\Delta{L_1}[1+ 2\alpha\Delta{T}^{2}]\)
4. \(\Delta{L_1}[1+ \alpha\Delta{T}]\)
Given \(T_3+T_1 =2T_2\) and \(T_2-T_1=\Delta{T},\) the value of \(\Delta{L}_2\) is:
1. \(\Delta{L_1}[1+ 2\alpha^{2}(\Delta{T})^{2}]\)
2. \(\Delta{L_1}[1+ \alpha^{2}(\Delta{T})^{2}]\)
3. \(\Delta{L_1}[1+ 2\alpha\Delta{T}^{2}]\)
4. \(\Delta{L_1}[1+ \alpha\Delta{T}]\)
Subtopic: Thermal Expansion |
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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of \(120~\text{cm}\) at \(30^{\circ}\text{C}\). The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6} /{ }^{\circ} \text{C}\) and \(1.2 \times 10^{-5} /{ }^{\circ} \text{C},\) respectively. The length of this composite rod when its temperature is raised to \(100^{\circ}\text{C}\), is: (in cm)
1. \(120.20\)
2. \(120.15\)
3. \(120.03\)
4. \(120.06\)
1. \(120.20\)
2. \(120.15\)
3. \(120.03\)
4. \(120.06\)
Subtopic: Thermal Expansion |
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A brass wire of length \(2~\text m\) and radius \(1~\text{mm}\) at \(27^\circ \text{C}\) is held taut between two rigid supports. Initially it was cooled to a temperature of \(–43^\circ \text{C}\) creating a tension \(T\) in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to \(1.4T,\) is: (in \(^\circ \text{C}\))
1. \(-86\)
2. \(-71\)
3. \(-65\)
4. \(-80\)
1. \(-86\)
2. \(-71\)
3. \(-65\)
4. \(-80\)
Subtopic: Thermal Expansion |
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Consider a rectangular sheet of solid material of length \(l = 9 \text{ cm} \) and width \(d = 4 ~\text{cm.} \) The coefficient of linear expansion is \(\alpha = 3.1 \times 10^{-5} ~\text{K} ^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \( m = 0.1~\text{kg} \) and the specific heat capacity \(C_v = 900 ~\text{Jkg}^{-1}~ \text{K}^{-1} .\) If the amount of heat supplied to the material is \(8.1 × 10^2 ~\text{J}\) then change in area of the rectangular sheet is: (in \(\text{m}^2\))
1. \(6.0\times10^{-7}\)
2. \(4.0\times10^{-7}\)
3. \(2.0\times10^{-6}\)
4. \(3.0\times10^{-7}\)
1. \(6.0\times10^{-7}\)
2. \(4.0\times10^{-7}\)
3. \(2.0\times10^{-6}\)
4. \(3.0\times10^{-7}\)
Subtopic: Thermal Expansion |
Level 4: Below 35%
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At the temperature \(25^\circ \text {C}\) resistance of the wire \({AB}\) is \(3~\Omega.\) Now the wire is cooled at the rate of \(2^\circ ~\text{C/s}.\) After \(10\) sec the deflection in galvanometer is zero, then the temperature coefficient of resistance of the wire \({AB}\) is:
1. \(1\times 10^{-3}\)
2. \(1\times 10^{-2}\)
3. \(1\times 10^{-4}\)
4. \(1\times 10^{-5}\)
1. \(1\times 10^{-3}\)
2. \(1\times 10^{-2}\)
3. \(1\times 10^{-4}\)
4. \(1\times 10^{-5}\)
Subtopic: Thermal Expansion |
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Two resistances have a coefficient of variation of resistivity \( \alpha _1\) and \( \alpha _2\) have equal resistance. The equivalent temperature coefficient of resistivity in series and parallel combinations are:
| 1. | \(\dfrac{\alpha_1+\alpha_2}{2}, ~ \alpha_1+\alpha_2\) | 2. | \(\alpha_1+\alpha_2,~ \alpha_1+\alpha_2\) |
| 3. | \(\alpha_1+\alpha_2,~ \dfrac{\alpha_1+\alpha_2}{2}\) | 4. | \(\dfrac{\alpha_1+\alpha_2}{2},~\dfrac{\alpha_1+\alpha_2}{2}\) |
Subtopic: Thermal Expansion |
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The resistance of the platinum wire at the ice point and steam point are \(10 ~\Omega\) and \(2~ \Omega\) respectively. After that wire is dipped in a hot bath of temperature \(400^\circ \text C.\) The resistance of the wire at a temperature of \(400^\circ \text C\) is:
1. \(32~\Omega\)
2. \(28~\Omega\)
3. \(42~\Omega\)
4. \(34~\Omega\)
1. \(32~\Omega\)
2. \(28~\Omega\)
3. \(42~\Omega\)
4. \(34~\Omega\)
Subtopic: Thermal Expansion |
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A uniform rectangular plate has a circular hole of diameter \(d\) as shown in the figure. The coefficient of linear expansion of the plate is \(\alpha.\) What will be the change in the diameter of the hole if the temperature of the plate is increased by \(\Delta T?\)
| 1. | \(2\alpha \Delta T\) | 2. | \(d\alpha \Delta T\) |
| 3. | \(\dfrac{d}{2}\alpha \Delta T\) | 4. | \(3\alpha \Delta T\) |
Subtopic: Thermal Expansion |
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A solid metallic cube having a total surface area of 24 m2 is uniformly heated. If its temperature is increased by 10°C, the increase in the volume of the cube is: ( Given \(: \alpha=5.0 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}\))
1. \(2.4 \times 10^6 \mathrm{~cm}^3 \)
2. \(1.2 \times 10^5 \mathrm{~cm}^3 \)
3. \(6.0 \times 10^4 \mathrm{~cm}^3 \)
4. \(4.8 \times 10^5 \mathrm{~cm}^3\)
1. \(2.4 \times 10^6 \mathrm{~cm}^3 \)
2. \(1.2 \times 10^5 \mathrm{~cm}^3 \)
3. \(6.0 \times 10^4 \mathrm{~cm}^3 \)
4. \(4.8 \times 10^5 \mathrm{~cm}^3\)
Subtopic: Thermal Expansion |
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At what temperature a gold ring of diameter \(6.230~\text{cm}\) be heated so that it can be fitted on a wooden bangle of diameter \(6.241~\text{cm}?\) Both diameters have been measured at room temperature \((27^\circ \text{C}) .\) (Given: coefficient of linear thermal expansion of gold, \(\alpha_L = 1.4 \times 10^{-5} \text{K}^{-1}\))
| 1. | \(125.7^\circ\text{C}\) | 2. | \(91.7^\circ\text{C}\) |
| 3. | \(425.7^\circ\text{C}\) | 4. | \(152.7^\circ\text{C}\) |
Subtopic: Thermal Expansion |
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