Mechanical Properties of Solids

18 NEET-UG practice questions on Mechanical Properties of Solids, part of Physics. The first 18 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
Arrange these points on the stress-strain curve of a ductile metal in the order in which they are reached as the strain increases. A. Fracture point B. Yield point C. Proportional limit D. Point of ultimate tensile strength
1. AB, D, C, A
2. BB, C, D, A
3. CC, B, D, A
4. DC, D, B, A
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Answer: C · C, B, D, A
Stress is proportional to strain up to the proportional limit. The yield point comes next, where plastic behaviour begins. Stress then rises to its greatest value, the ultimate tensile strength, and the wire finally breaks at the fracture point.
- A: This puts the proportional limit after the plastic region.
- B: The proportional limit comes before the yield point.
- D: Ultimate strength lies beyond the yield point, not before it.
Remember this
The maximum stress occurs before fracture; between these two points the stress falls as the wire thins.
Question 2 · Easy
In an experiment to find Young's modulus, a wire 2 m long with a cross-section of 1 mm² stretches by 1 mm under a load of 100 N. What value of Young's modulus do these readings give?
1. A2 × 10⁸ Pa
2. B5 × 10¹⁰ Pa
3. C2 × 10⁵ Pa
4. D2 × 10¹¹ Pa
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Answer: D · 2 × 10¹¹ Pa
Y = FL/(A ΔL) = (100 × 2)/(10⁻⁶ × 10⁻³) = 2 × 10¹¹ Pa.
- A: This does not convert the extension from millimetres to metres.
- B: This divides by the length instead of multiplying by it.
- C: This does not convert the area from mm² to m².
Remember this
Convert to SI first: 1 mm² = 10⁻⁶ m² and 1 mm = 10⁻³ m.
Question 3 · Medium
A sealed 2 litre sample of a liquid of bulk modulus 2 × 10⁹ Pa experiences a pressure rise of 4 × 10⁶ Pa. By how much does its volume decrease?
1. A2 cm³
2. B1 cm³
3. C0.4 cm³
4. D4 cm³
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Answer: D · 4 cm³
B = Δp/(ΔV/V), so ΔV/V = 4 × 10⁶/(2 × 10⁹) = 2 × 10⁻³. Then ΔV = 2000 cm³ × 2 × 10⁻³ = 4 cm³.
- A: This takes the original volume as 1 litre.
- B: This divides the strain by the 2 litres instead of multiplying.
- C: This makes a power-of-ten slip in the conversion from litres to cm³.
Remember this
Volumetric strain = Δp/B; multiply it by the original volume to get the volume change.
Question 4 · Medium
Load against extension is plotted for a wire 2 m long with a cross-section of 1 mm². What is the Young's modulus of its material?
Figure: MedExams
1. A2 × 10¹¹ Pa
2. B2 × 10⁵ Pa
3. C1 × 10¹¹ Pa
4. D2 × 10⁸ Pa
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Answer: A · 2 × 10¹¹ Pa
From the graph, 40 N gives 0.4 mm. Stress = 40/10⁻⁶ = 4 × 10⁷ Pa and strain = (0.4 × 10⁻³)/2 = 2 × 10⁻⁴, so Y = 2 × 10¹¹ Pa. Direct use of Y = FL/(AΔL) gives 80/(4 × 10⁻¹⁰), the same value.
- B: Leaves the area in mm², not converting it to m².
- C: Leaves out the wire's length of 2 m.
- D: Treats the extension in mm without converting it to metres.
Remember this
Y = FL/(AΔL) = (slope of load-extension) × L/A, in SI units.
Question 5 · Easy
Match List-I with List-II for the stress-strain curve of a metal wire shown. List-I (Point on the curve) A. P B. Q C. R D. S List-II (What it marks) I. Fracture point II. Proportional limit III. Ultimate tensile strength IV. Yield point
Figure: MedExams
1. AA-IV, B-II, C-III, D-I
2. BA-II, B-IV, C-III, D-I
3. CA-II, B-III, C-IV, D-I
4. DA-II, B-IV, C-I, D-III
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Answer: B · A-II, B-IV, C-III, D-I
Hooke's law holds on the straight part up to P, the proportional limit. Q, just beyond, is the yield point. The peak R is the ultimate tensile strength, and the wire breaks at S.
- A: Interchanges the proportional limit and the yield point.
- C: Interchanges the yield point and the peak stress.
- D: Places fracture at the peak, though the wire breaks later.
Remember this
Going up the curve: proportional limit, yield point, ultimate strength, then fracture.
Question 6 · Hard
A light rigid rod hangs from wires A and B of equal length and equal cross-section, and load W is hung at distance x from wire A (drawing not to scale). For what value of x does the rod stay horizontal?
Figure: MedExams
1. A45 cm
2. B18 cm
3. C30 cm
4. D60 cm
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Question 7 · Easy
Steel is said to be more elastic than rubber. This means that, for the same stress,
1. ASteel shows a smaller strain, so its Young's modulus is larger
2. BSteel shows a smaller strain, so its Young's modulus is smaller
3. CSteel shows a larger strain, so its Young's modulus is larger
4. DSteel stretches more before it breaks
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Question 8 · Hard
A steel wire (Y = 2 × 10¹¹ Pa) and a brass wire (Y = 1 × 10¹¹ Pa), of equal length L and equal cross-sectional area, are joined end to end and hung vertically with a load at the bottom. Treated as a single wire of length 2L, what is the effective Young's modulus of the combination? (Neglect the weights of the wires.)
1. A1.5 × 10¹¹ Pa
2. B3 × 10¹¹ Pa
3. C1.33 × 10¹¹ Pa
4. D0.67 × 10¹¹ Pa
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Question 9 · Medium
A wire of Young's modulus 2 × 10¹¹ Pa is under a tensile stress of 2 × 10⁸ Pa, within its elastic limit. Find the elastic potential energy stored per unit volume of the wire.
1. A2 × 10⁵ J/m³
2. B1 × 10⁵ J/m³
3. C1 × 10⁸ J/m³
4. D4 × 10⁵ J/m³
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Question 10 · Medium
A steel wire 2 m long, of cross-sectional area 1 mm², hangs vertically and a 100 N load is attached to its lower end. Taking Young's modulus of steel as 2 × 10¹¹ N/m², how much elastic potential energy is stored in the wire?
1. A0.025 J
2. B50 J
3. C0.1 J
4. D0.05 J
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Question 11 · Easy
Poisson's ratio of a material is the ratio of
1. Alateral strain to longitudinal strain
2. Blongitudinal strain to lateral strain
3. Clongitudinal stress to longitudinal strain
4. Dshearing stress to shearing strain
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Question 12 · Medium
Two wires, P and Q, are made of the same steel. P is twice as long as Q and has half its diameter. How do their Young's moduli compare?
1. AP has twice the Young's modulus of Q
2. BP has one-eighth the Young's modulus of Q
3. CP has eight times the Young's modulus of Q
4. DThey are equal, since Young's modulus depends only on the material
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Question 13 · Hard
Wires A and B are made of the same material. B is twice as long as A and has twice its diameter. The same stretching force is applied to each. What is the ratio of the elastic energy stored in B to that stored in A?
1. A1 : 1
2. B1 : 2
3. C2 : 1
4. D1 : 4
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Question 14 · Hard
A steel wire of diameter d and a copper wire of diameter 2d are joined end to end and loaded. Young's modulus of steel is 2 × 10¹¹ N/m² and that of copper is 1 × 10¹¹ N/m². Ignoring the weight of the wires, what is the ratio of the strain in the steel wire to that in the copper wire?
1. A4
2. B1/2
3. C2
4. D1
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Question 15 · Medium
Two wires A and B are made of the same material. B has twice the length and twice the diameter of A. The same load is hung from each. What is the ratio of the extension of B to that of A?
1. A1/4
2. B1
3. C1/2
4. D2
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Question 16 · Medium
Match List-I with List-II. List-I (Situation) A. A wire stretched by a hanging load B. A solid ball lying deep under water C. The top face of a block pushed sideways while its base is fixed D. A pillar holding up a roof List-II (Kind of stress) I. Shearing stress II. Compressive stress III. Tensile stress IV. Hydraulic stress Choose the correct answer from the options given below.
1. AA-IV, B-III, C-I, D-II
2. BA-III, B-IV, C-I, D-II
3. CA-II, B-IV, C-I, D-III
4. DA-III, B-I, C-IV, D-II
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Question 17 · Medium
A metal cube of side 10 cm has its lower face fixed. A tangential force of 1000 N on its upper face moves that face sideways by 0.01 mm. What is the shear modulus of the metal?
1. A1 × 10⁵ Pa
2. B1 × 10⁸ Pa
3. C1 × 10⁹ Pa
4. D1 × 10¹⁰ Pa
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Question 18 · Easy
On the stress-strain curve of a metal wire, what is the stress called beyond which the wire no longer regains its original length when the load is removed?
1. AElastic limit (yield point)
2. BFracture point
3. CProportional limit
4. DUltimate tensile strength
Answer and explanation in LearnFree account

Mechanical Properties of Solids

Arrange these points on the stress-strain curve of a ductile metal in the order in which they are reached as the strain increases. A. Fracture point B. Yield point C. Proportional limit D. Point of ultimate tensile strength

In an experiment to find Young's modulus, a wire 2 m long with a cross-section of 1 mm² stretches by 1 mm under a load of 100 N. What value of Young's modulus do these readings give?

A sealed 2 litre sample of a liquid of bulk modulus 2 × 10⁹ Pa experiences a pressure rise of 4 × 10⁶ Pa. By how much does its volume decrease?

Load against extension is plotted for a wire 2 m long with a cross-section of 1 mm². What is the Young's modulus of its material?

Match List-I with List-II for the stress-strain curve of a metal wire shown. List-I (Point on the curve) A. P B. Q C. R D. S List-II (What it marks) I. Fracture point II. Proportional limit III. Ultimate tensile strength IV. Yield point

A light rigid rod hangs from wires A and B of equal length and equal cross-section, and load W is hung at distance x from wire A (drawing not to scale). For what value of x does the rod stay horizontal?

Steel is said to be more elastic than rubber. This means that, for the same stress,

A wire of Young's modulus 2 × 10¹¹ Pa is under a tensile stress of 2 × 10⁸ Pa, within its elastic limit. Find the elastic potential energy stored per unit volume of the wire.

A steel wire 2 m long, of cross-sectional area 1 mm², hangs vertically and a 100 N load is attached to its lower end. Taking Young's modulus of steel as 2 × 10¹¹ N/m², how much elastic potential energy is stored in the wire?

Poisson's ratio of a material is the ratio of

Two wires, P and Q, are made of the same steel. P is twice as long as Q and has half its diameter. How do their Young's moduli compare?

Wires A and B are made of the same material. B is twice as long as A and has twice its diameter. The same stretching force is applied to each. What is the ratio of the elastic energy stored in B to that stored in A?

A steel wire of diameter d and a copper wire of diameter 2d are joined end to end and loaded. Young's modulus of steel is 2 × 10¹¹ N/m² and that of copper is 1 × 10¹¹ N/m². Ignoring the weight of the wires, what is the ratio of the strain in the steel wire to that in the copper wire?

Two wires A and B are made of the same material. B has twice the length and twice the diameter of A. The same load is hung from each. What is the ratio of the extension of B to that of A?

A metal cube of side 10 cm has its lower face fixed. A tangential force of 1000 N on its upper face moves that face sideways by 0.01 mm. What is the shear modulus of the metal?

On the stress-strain curve of a metal wire, what is the stress called beyond which the wire no longer regains its original length when the load is removed?