## Expansion Of Solid And Liquids Multiple Choice Questions And Answers

**Question 1. When a hollow metallic sphere is heated, the volume of the cavity inside that sphere**

- Remains the same
- Decreases
- Increases

**Answer:** 3. Increases

**Question 2. If a solid metallic sphere is heated, which of the following quantities undergoes the highest percentage increase?**

- Length
- Area
- Volume
- Density

**Answer:** 3. Volume

**Question 3. A steel scale gives the correct reading at 10 °C. If the length of a rod is measured with the help of that scale at 30 °C then the measured length will be**

- Equal to the actual length
- Less than the actual length
- More than the actual length

**Answer:** 2. Less than the actual length

**Question 4. A platinum wire can easily be sealed in glass, because for glass and platinum**

- Densities are equal
- Melting points are equal
- Specific heats are equal
- Coefficients of linear expansion are equal

**Answer:** 4. Coefficients of linear expansion are equal

**Question 5. The ratio of lengths of two iron rods is 1 : 2 and that of their cross-sectional areas is 2 : 3 . What will be the ratio of their expansions in volume for the same rise in temperature?**

- 1:2
- 1:3
- 2:3
- 4:6

**Answer:** 2. 1:3

**Question 6. Three rods of iron form an isosceles triangle. What will be the change in the base angles of that triangle due to a rise in its temperature?**

- No change will occur
- Both the base angles will increase but the vertical angle will decrease
- Both the base angles will decrease but the vertical angle will increase
- No conclusion can be arrived at

**Answer:** 1. No change will occur

**Question 7. A brass disc just fits inside the hole of an iron plate, lb loosen the disc front the hole easily, which of the following operations would be more convenient? (coefficient of linear expansion of brass is more than that of iron).**

- The junction should be heated
- The junction should be cooled
- The junction should be hammered without heating or cooling it
- The junction should be heated first and then it should be dipped in water

**Answer:** 2. The junction should be cooled

**Question 8. An aluminium rod (coefficient of linear expansion α _{1}) of length l_{1} at 0°C is welded with a steel rod (coefficient of linear expansion α_{2}) of length to l_{2} form a composite rod of length (l_{1} + l_{2}). If. when heated through t°C, each rod increases in length by the same amount, then the value of \(\frac{l_1}{l_1+l_2}\) will be**

- \(\frac{a_1}{a_2}\)
- \(\frac{\alpha_2}{a_1}\)
- \(\frac{a_1}{\alpha_1+\alpha_2}\)
- \(\frac{\alpha_2}{\alpha_1+\alpha_2}\)

**Answer:** 4. \(\frac{\alpha_2}{\alpha_1+\alpha_2}\)

**Question 9. The coefficient of linear expansion of brass is 19 x 10 ^{-6 }°C^{-1}. If the area of a circular brass disc at 0°C is 25 cm² , then at 80°C its area will be**

- 25.038 cm²
- 25.076 cm²
- 25.114 cm²
- 25.38 cm²

**Answer:** 2. 25.076 cm²

**Question 10. The length of each steel rail of a line at 10°C is 25 m. What gap should be maintained between two successive rails so that up to 50°C they will not be strained? [coefficient of linear expansion of steel = 11 x 10 ^{-6} °C^{-1}]**

- 5.5 mm
- 8.25 mm
- 1.1 mm
- 1.65 mm

**Answer:** 3. 1.1 mm

**Question 11. Two similar iron and copper strips are riveted together at**

**20°C. What will be the nature of curvature of this bimetallic strip at 0°C and at 100°C? (The coefficient of linear expansion of copper is more than that of iron)**

- At both the temperatures the copper plate will be on the convex side
- At both the temperatures the iron plate will be on the convex side
- At 0°c the copper plate will be on the convex side but at 100cc, it will be on the concave side
- At 0°c the iron plate will be on the convex side but at 100°c it will be on the concave side.

**Answer:** 4. At 0°c the iron plate will be on the convex side but at 100°c it will be on the concave side.

**Question 12. In which of the following cases a bimetallic strip is not used?**

- Sealing of a platinum wire in glass
- Thermostat
- Fire alarm
- Compensated balance wheel of a watch

**Answer:** 1. Sealing of a platinum wire in glass

**Question 13. The length of a brass rod is to be measured at different temperatures. For this, the accuracy will be the highest if the scale is made of which material?**

- Wood
- Steel
- Brass
- Platinum

**Answer:** 1. Wood

**Question 14. Young’s modulus for the material of a rod is Y and its coefficient of linear expansion is α. A rod of length l and cross-section A of this material is kept in between two rigid supports and its temperature is increased by t °C. The force developed inside the rod is**

- lAYαt
- AYαt
- lYαt
- Yαt

**Answer:** 2. AYαt

**Question 15. Two rods of the same length are kept in between two rigid supports and their temperatures are increased by the same amount. What will be the relation between the Young’s moduli and coefficients of linear expansion of the rods, for equal thermal stresses generated in them?**

- \(\frac{Y_1}{Y_2}=\frac{\alpha_1}{\alpha_2}\)
- \(\frac{Y_1}{Y_2}=\sqrt{\frac{\alpha_1}{\alpha_2}}\)
- \(\frac{Y_1}{Y_2}=\frac{\alpha_2}{\alpha_1}\)
- \(\frac{Y_1}{Y_2}=\sqrt{\frac{\alpha_2}{\alpha_1}}\)

**Answer:** 3. \(\frac{Y_1}{Y_2}=\frac{\alpha_2}{\alpha_1}\)

**Question 16. When tire temperature of a metallic sphere is increased by 40°C then its volume increases by 0.24%. The coefficient of linear expansion of the metal in °C ^{-1} is**

- 2×10
^{-5} - 6×10
^{-5} - 18×10
^{-5} - 1.2×10
^{-5}

**Answer:** 1. 2×10^{-5}

**Question 17. The ratio of the lengths of two metallic rods is 2 : 3 and the ratio of the coefficients of linear expansion of their materials is 4 : 3. The ratio of their linear expansions for the same rise in temperature is**

- 1:2
- 2:3
- 3:4
- 8:9

**Answer:** 4. 8:9

**Question 18. A steel scale gives correct reading at t _{1} °C. With the help of this scale the distance between two points measures l’ at t_{2} °C. If the coefficient of linear expansion of steel is a then the actual length l between the two points is**

- \(l=l^{\prime}\)
- \(l=l^{\prime}\left[1+\alpha\left(t_2-t_1\right)\right]\)
- \(l=l^{\prime}\left[1-\alpha\left(t_2-t_1\right)\right]\)
- \(l=\frac{l^{\prime}\left[1+\alpha\left(t_2-t_1\right)\right]}{1+\alpha\left(t_2-t_1\right)}\)

**Answer:** 2. \(l=l^{\prime}\left[1+\alpha\left(t_2-t_1\right)\right]\)

**Question 19. Two spheres of the same material have the same radius but one is hollow while the other is solid. Both spheres are heated to same temperature. Then**

- The solid sphere expands more
- The hollow sphere expands more
- Expansion is same for both
- Nothing can be said about their relative expansion if their masses are not given

**Answer:** 3. Expansion is same for both

**Question 20. When a rod is heated but prevented from expanding the stress developed is independent of**

- Material of the rod
- Rise in temperature
- Length of the rod
- None of the above

**Answer:** 3. Length of the rod

**Question 21. A cylindrical metal rod of length L _{0} is shaped into a ring with a small gap as shown in Figure On heating the system**

- x decreases, r and d increase
- x and r increase, d decreases
- x, r and d all increase
- Data insufficient to arrive at a conclusion

**Answer**: 3. x, r and d all increase

**Question 22. At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimal when (the coefficient of linear expansion of bronze is greater than that of steel)**

- Only the block is heated
- Both block and pin are heated together
- Both block and pin are cooled together
- Only the pin is cooled

**Answer:** 4. Only the pin is cooled

**Question 23. When water is heated from 0°C to 50°C, density of water**

- Remains the same
- Decreases continually
- Increases continually
- Increases at first and then decreases

**Answer:** 4. Increases at first and then decreases

**Question 24. Due to anomalous expansion of water from 0°C to4°C, in cold countries**

- Entire water in a lake freezes to ice
- No part of water in a lake freezes to ice
- Aquatic animals can survive
- Oxygen content of water increases

**Answer:** 3. Aquatic animals can survive

**Question 25. The relation between real and apparent expansion of a liquid is**

- Real expansion = apparent expansion
- Real expansion < apparent expansion
- Real expansion > apparent expansion
- Depending on the nature of the liquid, sometimes apparent expansion and sometimes real expansion is greater

**Answer:** 3. Real expansion > apparent expansion

**Question 26. How many coefficients of expansion of a liquid is used in practice?**

- 1
- 2
- 3
- 4

**Answer:** 2. 2

**Question 27. The coefficient of real expansion of a liquid is γ and the coefficient of apparent expansion is γ’. Units of these are**

- both °C
^{-1} - both m
^{3 }°C^{-1} - °C
^{-1}for y and m^{3}· °C^{-1}for γ’ - m
^{3}°C^{-1}for γ and °C^{-1}for γ’

**Answer:** 1. both °C_1

**Question 28. If a liquid having a coefficient of volume expansion a, kept in a container having coefficient of linear expansion α/3, is heated, then the level of the liquid will**

- Rise
- Fall
- Remain the same
- Remain almost the same

**Answer:** 3. Remain the same

**Question 29. The coefficient of volume expansion of a liquid is**

- Positive for all liquids
- Negative for all liquids
- Negative for water from 0°c to 4°c but positive for other liquids
- Positive for water from 0°c to 4°c but negative for other liquids

**Answer:** 3. Negative for water from 0°c to 4°c but positive for other liquids

**Question 30. A vessel is partly filled with a liquid at 0°C. The condition for which the volume of the remaining part of the vessel remains unchanged is**

- Expansion of the entire vessel = real expansion of the liquid in the vessel
- Expansion of the remaining part of the vessel = real expansion of the liquid in the vessel
- Expansion of the entire vessel = apparent expansion of the liquid in the vessel
- Expansion of the remaining part of the vessel = apparent expansion of the liquid in the vessel

**Answer:** 1. Expansion of the entire vessel = real expansion of the liquid in the vessel

**Question 31. Apparent weight of a body immersed in water at 20°C is W _{1}. When temperature is increased to 40°C, the apparent weight becomes. In this case**

- For different solids W
_{2}may be greater than or less than W_{1} - W
_{2}is always equal to W_{1} - W
_{2}is always less than W_{1} - W
_{2}is always greater than W_{1}

Answer: 4. W_{2} is always greater than W_{1}

**Question 32. Apparent weights of a body immersed in a liquid at the temperature t _{1} is W_{1} and temperature t_{2} is W_{2}. Coefficients of volume expansion of the liquid and the solid are γ and γ_{s} respectively. The value of W_{2} – W_{1} will be**

- proportional to \(\left(\gamma-\gamma_s\right)\left(t_2-t_1\right)\)
- proportional to \(\frac{\gamma-\gamma_s}{t_2-t_1}\)
- proportional to \(\frac{t_2-t_1}{\gamma-\gamma_s}\)
- proportional to \(\frac{1}{\left(\gamma-\gamma_5\right)\left(t_2-t_1\right)}\)

**Answer:** 1. proportional to \(\left(\gamma-\gamma_s\right)\left(t_2-t_1\right)\)

**Question 33. Apparent weight of a piece of metal immersed in water at 0°C is 100 g and at 50°C is 100.5 g. What will be the apparent weight at 20 °C?**

- 100.1 g
- 100.2 g
- 100.3 g
- 100.4 g

**Answer:** 2. 100.2 g

**Question 34. A block of wood is floating on water. If the temperature is increased the apparent weight of the block of wood**

- Will remain the same
- Will increase
- Will decrease
- May increase or decrease

**Answer:** 1. Will remain the same

**Question 35. The coefficient of apparent expansion of a liquid for two different vessels A and B are γ _{1} and γ_{2 }respectively. If the coefficient of linear expansion of the material of the vessel A is a, then the coefficient of linear expansion of the material of the vessel B will be**

- \(\frac{\alpha \gamma_1 \gamma_2}{\gamma_1+\gamma_2}\)
- \(\frac{\gamma_1-\gamma_2}{2 \alpha}\)
- \(\frac{\gamma_1-\gamma_2+\alpha}{3}\)
- \(\frac{\gamma_1-\gamma_2}{3}+\alpha\)

**Answer:** 4. \(\frac{\gamma_1-\gamma_2}{3}+\alpha\)

**Question 36. A glass is fully filled with water at 4°C. Water overflows when the glass is**

- Cooled but not when heated
- Heated but not when cooled
- Both cooled or heated
- First heated then cooled

**Answer:** 3. Both cooled or heated

**Question 37. Weight of a piece of metal immersed in alcohol at 0°C is W _{1} and at 59 °C is W_{2}. The coefficient of volume expansion of the metal is less than the coefficient of volume expansion of alcohol If the density of the metal is greater than that of alcohol then**

- W
_{1 }>W_{2} - W
_{1 }= W_{2} - W
_{1 }< W_{2} - W
_{2 }= W_{1}/2

**Answer:** 3. W_{1 }< W_{2}

**Question 38. The coefficient of volume expansion of a liquid is γ and its density at 0°C is ρ. If the temperature is increased to t°C then the change in density will be**

- \(\frac{\rho(1-\gamma t)}{\gamma t}\)
- \(-\frac{\rho(1+\gamma t)}{\gamma t}\)
- \(\frac{\rho \gamma t}{1-\gamma t}\)
- \(-\frac{\rho \gamma t}{1-\gamma t}\)

**Answer:** 4. \(-\frac{\rho \gamma t}{1-\gamma t}\)

**Question 39. Surface of a lake is at 2C. Find the temperature of the bottom of the lake**

- 2°C
- 3°C
- 4°C
- 1°C

**Answer:** 3. 4°C

**Question 40. The coefficient of real expansion of a liquid is γ and the coefficient of linear expansion of the material of the containing vessel is a. Then die condition for no apparent expansion of the liquid in that vessel is**

- γ = a
- γ = 3a
- γ < a
- γ >3a

**Answer:** 2. γ = 3a

**Question 41. Two vessels are filled with water at the same temperature. If one vessel is heated and the other is cooled, then in both the cases water overflows. The initial temperature of water in both the vessels was**

- 273°C
- 273°K
- 277°C
- 277°K

**Answer:** 4. 277°K

**Question 42. The coefficient of real expansion of mercury is γ and the coefficient of linear expansion of glass is α. The mercury thread, enclosed in a glass tube of uniform bore, expands linearly due to rise in temperature. The effective coefficient of expansion will be**

- \(\frac{\gamma}{3}\)
- \(\frac{\gamma-3 \alpha}{3}\)
- \(\frac{\gamma-2 a}{3}\)
- \(\gamma-2 a\)

**Answer:** 4. \(\gamma-2 a\)

**Question 43. The coefficient of volume expansion of mercury is 18 x 10 ^{-5} °C^{-1} and the coefficient of linear expansion of copper and glass are 17 x 10^{-6 °}C^{-1} and 9 x 10^{-6} °C^{-1} respectively. If mercury is kept first in the copper vessel and then in the glass vessel, then**

- Coefficient of apparent expansion of mercurv in the first case will be less
- Coefficient of apparent expansion of mercury in the first case will be greater
- Coefficient of real expansion of mercury in the first case will be less
- Coefficient of real expansion of mercury in the first case will be greater

**Answer:** 1. Coefficient of apparent expansion of mercury in the first case will be less

**Question 44. To measure the height of the mercury column in a barometer, a brass scale is attached with it. Coefficient of real expansion of mercury is γ and the coefficient of linear expansion of brass is α. Due to rise in temperature, the effective coefficient at which the barometer reading increases is**

- γ
- γ+a
- γ-a
- γ-2a

**Answer:** 3. γ-a

**Question 45. A uniform pressure p is applied on each face of a solid cube. What will be the rise in temperature of the cube so that it regains its original volume? (Given, bulk modulus = B and coefficient of volume expansion = γ for the material of the cube.)**

- \(\frac{p}{(B-p) r}\)
- \(\frac{p r}{B}\)
- \(\frac{p B}{r}\)
- \(\frac{B r}{p}\)

**Answer:** 1. \(\frac{p}{(B-p) r}\)

**In this type of questions, more than one options are correct.**

**Question 46. If α, β and γ are coefficients of linear, surface and volume expansion respectively, then**

- (β/α) = (1/2)
- (β/γ) = (2/3)
- (γ/β) = (3/1)
- (β/α) = (γ/β)

**Answer:**

2. (β/γ) = (2/3)

3. (γ/β) = (3/1)

**Question 47. In case of a metal scale**

- The distance between any two scale divisions does not vary with temperature
- The distance between any two scale divisions increases in the ratio of 1: (1 + αt) at a higher temperature
- The distance between any two scale divisions is higher than the true distance in the ratio (1 + αt): 1 at a lower temperature
- None of the above

**Answer:**

2. The distance between any two scale divisions increases in the ratio of 1: (1 + αt) at a higher temperature

3. The distance between any two scale divisions is higher than the true distance in the ratio (1 + αt): 1 at a lower temperature

**Question 48. If the temperature of a rod is increased from θ to θ’ thermal strain in it will depend on**

- Young’s modulus, Y
- Coefficient of linear expansion, a
- Temperature difference, (θ’-θ)
- None of these

**Answer:**

- Young’s modulus, Y
- Coefficient of linear expansion, a
- Temperature difference, (θ’-θ)

**Question 49. Two identical beakers A and B are filled with water to the same level at 4 °C. If A is heated while B is cooled, then**

- Water level in A will rise
- Water level in B will rise
- Water level in A will fall
- Water level in B will fall

**Answer:**

- Water level in A will rise
- Water level in B will rise

**Question 50. Due to thermal expansion, with rise in temperature**

- Metallic scale reading becomes less than the true value
- Pendulum clock becomes fast
- A floating body sinks a little more
- The weight of a body in a liquid increases

**Answer:**

1. Metallic scale reading becomes less than the true value

3. A floating body sinks a little more

**Question 51. A bimetallic strip is formed out of identical strips one of copper and the other of brass. The coefficients of linear expansion of the two metals are α _{C} and α_{B}. On heating, the temperature of the strip goes up by ΔT and the strip bends to form an arc of radius of curvature R. Then R Is**

- Proportional to Δt
- Inversely proportional to Δt
- Proportional to \(\left|\alpha_b-\alpha_c\right|\)
- Inversely proportional to \(\left|\alpha_b-\alpha_c\right|\)

**Answer:**

2. Inversely proportional to Δt

4. Inversely proportional to \(\left|\alpha_b-\alpha_c\right|\)

**Question 52. A uniform metallic circular disc of mass M and radius R, mounted on frictionless bearings, is rotating at an angular speed a> about an axis passing through its centre and perpendicular to its plane. The temperature of the disc is then increased by Δt. If a is the coefficient of linear expansion of the metal**

- The moment of inertia increases by MR²αΔt
- The moment of inertia remains unchanged
- The angular velocity increases by 2αwΔt
- The angular velocity decreases by 2αwΔt

**Answer:**

2. The moment of inertia remains unchanged

4. The angular velocity decreases by 2αwΔt