Chapter 8: Mechanical Properties of Solids Short Questions | physics Class 11 CBSE

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Chapter 8: Mechanical Properties of Solids Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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Define stress and state its SI unit and dimensional formula.

Stress is the restoring force developed per unit area inside a deformed body when a deforming force is applied.
The SI unit of stress is N m⁻² or Pascal (Pa).
Its dimensional formula is [ML⁻¹T⁻²].

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Question 2

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Distinguish between elasticity and plasticity with one example of each.

Elasticity is the property by which a body regains its original size and shape after the deforming force is removed; a helical spring is an example.
Plasticity is the property by which a body undergoes permanent deformation and does not regain its original shape; putty or mud is an example.
The deformation caused in an elastic material is called elastic deformation, while that in a plastic material is called plastic deformation.

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Question 3

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What is longitudinal strain? Write its formula and state whether it has units.

Longitudinal strain is the ratio of the change in length (ΔL) to the original length (L) of a body subjected to tensile or compressive stress.
Longitudinal strain = ΔL/L.
Since it is a ratio of two lengths, it is dimensionless and has no units or dimensional formula.

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Question 4

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State Hooke's law and identify the constant of proportionality in the stress-strain relationship.

Hooke's law states that for small deformations, stress is directly proportional to strain: stress ∝ strain.
This can be written as stress = k × strain, where k is the proportionality constant.
The constant k is known as the modulus of elasticity and is a characteristic property of the material.

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Question 5

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Define shearing strain and write its expression in terms of angular displacement.

Shearing strain is the ratio of the relative displacement (Δx) between opposite faces of a body to the length of the body (L): shearing strain = Δx/L.
It can also be expressed as tan θ, where θ is the angular displacement of the body from its original (vertical) position.
Since θ is usually very small, shearing strain ≈ tan θ ≈ θ (in radians).

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Question 6

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Define Young's modulus and write its formula in terms of force, area, and dimensions of the wire.

Young's modulus (Y) is defined as the ratio of tensile (or compressive) stress to the longitudinal strain within the elastic limit.
Y = σ/ε = (F/A)/(ΔL/L) = (F × L)/(A × ΔL).
Its SI unit is N m⁻² or Pascal (Pa), the same as that of stress, since strain is dimensionless.

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Question 7

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Why is steel preferred over copper, brass, and aluminium for heavy-duty machines and structural designs?

Steel has a much larger Young's modulus (200×10⁹ N m⁻²) compared to copper (110×10⁹ N m⁻²), brass, and aluminium (70×10⁹ N m⁻²).
A material with a larger Young's modulus requires a greater force to produce the same strain, meaning steel is more resistant to deformation.
For example, to produce 0.1% strain in a 0.1 cm² wire, steel requires 2000 N whereas aluminium requires only 690 N, so steel is more elastic in the scientific sense.

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Question 8

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Define shear modulus (modulus of rigidity) and write its formula.

Shear modulus (G), also called the modulus of rigidity, is defined as the ratio of shearing stress to the corresponding shearing strain.
G = (F/A)/(Δx/L) = (F × L)/(A × Δx), or equivalently G = F/(A × θ).
Its SI unit is N m⁻² or Pa, and for most materials G ≈ Y/3.

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Question 9

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Define bulk modulus. Why does the formula B = −p/(ΔV/V) contain a negative sign?

Bulk modulus (B) is the ratio of hydraulic stress (pressure p) to the volume strain (ΔV/V): B = −p/(ΔV/V).
The negative sign indicates that an increase in pressure (positive p) causes a decrease in volume (negative ΔV), so that B remains positive.
Its SI unit is N m⁻² or Pa, the same as pressure.

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Question 10

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What is compressibility? How does it relate to bulk modulus, and which state of matter is most compressible?

Compressibility (k) is the reciprocal of bulk modulus: k = 1/B = −(1/Δp) × (ΔV/V).
It is defined as the fractional change in volume per unit increase in pressure.
Gases are the most compressible — they are about a million times more compressible than solids, because gas molecules are very poorly coupled to their neighbours.

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Question 11

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Define Poisson's ratio. Is it a scalar, vector, or dimensionless quantity? State its value for steel.

Poisson's ratio is the ratio of lateral strain (Δd/d) to longitudinal strain (ΔL/L) in a stretched wire: μ = (Δd/d)/(ΔL/L).
It is a pure number — dimensionless — because it is the ratio of two strains; it has no units.
For steels, the value of Poisson's ratio lies between 0.28 and 0.30.

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Question 12

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Write the expression for elastic potential energy per unit volume stored in a stretched wire and identify each term.

The elastic potential energy per unit volume of a stretched wire is u = ½σε, where σ is the stress and ε is the strain.
This energy is stored as work done against the inter-atomic forces during elongation of the wire.
It can also be written as u = ½ × Young's modulus × strain², emphasising its dependence on the modulus and the square of the strain.

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Question 13

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What are elastomers? Give two examples and state how their stress-strain behaviour differs from metals.

Elastomers are substances that can be stretched to cause very large strains and still return to their original shape; examples include rubber and the elastic tissue of the aorta.
Unlike metals, elastomers do not obey Hooke's law over most of their elastic region — the stress-strain relationship is highly non-linear.
Additionally, there is no well-defined plastic region in elastomers; they can sustain very large elastic strains without permanent deformation.

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Chapter sections

Chapter 8: Mechanical Properties of Solids | Short Questions

Define stress and state its SI unit and dimensional formula.

Distinguish between elasticity and plasticity with one example of each.

What is longitudinal strain? Write its formula and state whether it has units.

State Hooke's law and identify the constant of proportionality in the stress-strain relationship.

Define shearing strain and write its expression in terms of angular displacement.

Define Young's modulus and write its formula in terms of force, area, and dimensions of the wire.

Why is steel preferred over copper, brass, and aluminium for heavy-duty machines and structural designs?

Define shear modulus (modulus of rigidity) and write its formula.

Define bulk modulus. Why does the formula B = −p/(ΔV/V) contain a negative sign?

What is compressibility? How does it relate to bulk modulus, and which state of matter is most compressible?

Define Poisson's ratio. Is it a scalar, vector, or dimensionless quantity? State its value for steel.

Write the expression for elastic potential energy per unit volume stored in a stretched wire and identify each term.

What are elastomers? Give two examples and state how their stress-strain behaviour differs from metals.

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