Properties of Solids flash cards

1. 1.What is deforming force?

   An external force applied on a body that tends to change its size, shape, or both (its configuration). It is opposed by internal restoring forces.

   Hint: It changes configuration.

2. 2.Define elasticity.

   The property of a body by virtue of which it regains its original size and shape after the removal of the deforming force.

   Hint: Regains original shape.

3. 3.Define plasticity.

   The property of a body by virtue of which it does NOT regain its original configuration after the deforming force is removed; it retains the deformed state. Example: putty, mud.

   Hint: Opposite of elasticity.

4. 4.Which is more elastic, steel or rubber?

   Steel is more elastic than rubber. For the same applied stress, steel develops a smaller strain (larger restoring force / larger Young's modulus), so it opposes deformation more strongly.

   Hint: Smaller strain ⇒ more elastic.

5. 5.Define stress and give its SI unit.

   Stress = restoring force per unit area of cross-section developed inside the body: $\sigma = F/A$. SI unit: $\text{N m}^{-2}$ or pascal ($\text{Pa}$). Dimensions: $[ML^{-1}T^{-2}]$.

   Hint: Force per unit area.

6. 6.Define strain and state its unit.

   Strain = ratio of change in configuration to the original configuration (e.g. $\Delta L/L$). It is a pure ratio, so it is dimensionless and has no unit.

   Hint: Ratio of change to original.

7. 7.What are the three types of stress?

   (1) Longitudinal (normal) stress — tensile or compressive, force perpendicular to area; (2) Volume (hydraulic/bulk) stress — pressure acting normally over the whole surface; (3) Shearing (tangential) stress — force parallel to the surface.

   Hint: Longitudinal, volume, shear.

8. 8.Distinguish tensile and compressive stress.

   Both are longitudinal (normal) stresses. Tensile stress stretches the body (length increases); compressive stress squeezes it (length decreases). Force acts perpendicular to the cross-section in both.

   Hint: Stretch vs squeeze.

9. 9.Define longitudinal strain.

   Longitudinal strain = change in length per unit original length: $\dfrac{\Delta L}{L}$. It accompanies tensile or compressive (normal) stress.

   Hint: $\Delta L/L$.

10. 10.Define volumetric (bulk) strain.

    Volumetric strain = change in volume per unit original volume: $\dfrac{\Delta V}{V}$. It results from hydraulic (volume) stress.

    Hint: $\Delta V/V$.

11. 11.Define shear strain.

    Shear strain is the angle $\theta$ (in radians) through which a face of the body is displaced, given by $\tan\theta = \dfrac{\Delta x}{L}$, where $\Delta x$ is the relative displacement and $L$ the height. For small angles, $\theta \approx \Delta x/L$.

    Hint: Angle of tilt $\theta$.

12. 12.What is shearing stress?

    Shearing (tangential) stress = tangential force applied per unit area of the surface, $\sigma_s = F/A$, where $F$ acts parallel (tangential) to the surface. It changes shape without changing volume.

    Hint: Tangential force / area.

13. 13.State Hooke's law.

    Within the elastic limit, stress is directly proportional to strain: $\text{stress} \propto \text{strain}$, i.e. $\text{stress} = E \times \text{strain}$, where $E$ (modulus of elasticity) is a constant for the material.

    Hint: Stress ∝ strain (small deformations).

14. 14.What is a modulus of elasticity?

    The ratio of stress to strain within the elastic limit: $E = \dfrac{\text{stress}}{\text{strain}}$. It has the same units as stress ($\text{N m}^{-2}$ or $\text{Pa}$) since strain is dimensionless.

    Hint: Stress/strain constant.

15. 15.Define Young's modulus $Y$.

    $Y = \dfrac{\text{longitudinal (tensile) stress}}{\text{longitudinal strain}} = \dfrac{F/A}{\Delta L/L} = \dfrac{FL}{A\,\Delta L}$. It measures resistance to change in length.

    Hint: Tensile stress / long. strain.

16. 16.Write Young's modulus for a wire of length $L$, area $A$, stretched $\Delta L$ by force $F$.

    $Y = \dfrac{FL}{A\,\Delta L}$. For a wire of radius $r$, $A = \pi r^2$, so $Y = \dfrac{FL}{\pi r^2\,\Delta L}$.

    Hint: $FL/(A\Delta L)$.

17. 17.Define bulk modulus $B$.

    $B = -\dfrac{\text{volume stress}}{\text{volume strain}} = -\dfrac{\Delta P}{\Delta V/V} = -\dfrac{V\,\Delta P}{\Delta V}$. The minus sign shows volume decreases as pressure increases.

    Hint: $-\Delta P/(\Delta V/V)$.

18. 18.Why is there a negative sign in the bulk modulus formula?

    Because an increase in pressure ($\Delta P > 0$) causes a decrease in volume ($\Delta V < 0$). The negative sign keeps $B$ positive.

    Hint: $\Delta V$ and $\Delta P$ have opposite signs.

19. 19.Define compressibility.

    Compressibility is the reciprocal of the bulk modulus: $k = \dfrac{1}{B}$. It measures how easily a material's volume is reduced under pressure. Unit: $\text{Pa}^{-1}$.

    Hint: $1/B$.

20. 20.Define shear (rigidity) modulus $\eta$ (or $G$).

    $\eta = \dfrac{\text{shearing stress}}{\text{shear strain}} = \dfrac{F/A}{\theta} = \dfrac{F}{A\theta}$. It measures resistance to change in shape.

    Hint: Shear stress / shear strain.

21. 21.Which modulus applies to solids, liquids, and gases?

    Young's modulus and shear modulus apply only to solids (they resist changes in length/shape). Bulk modulus applies to solids, liquids and gases (all resist change in volume).

    Hint: Only B works for fluids.

22. 22.Why do fluids have no Young's or shear modulus?

    Liquids and gases cannot sustain a fixed length or shape — they flow under tangential (shear) stress and take the shape of their container. So longitudinal and shear strains are not defined; only volume elasticity (bulk modulus) exists.

    Hint: Fluids flow, don't resist shear.

23. 23.Define Poisson's ratio $\sigma$.

    When a wire is stretched, it becomes longer and thinner. Poisson's ratio = $\sigma = -\dfrac{\text{lateral strain}}{\text{longitudinal strain}} = \dfrac{-\Delta d/d}{\Delta L/L}$. It is dimensionless.

    Hint: Lateral strain / longitudinal strain.

24. 24.What is the theoretical and practical range of Poisson's ratio?

    Theoretical limits: $-1$ to $+0.5$. For most common materials the practical value lies between about $0.2$ and $0.4$. It has no units.

    Hint: Practically 0.2–0.4.

25. 25.What is lateral strain?

    Lateral strain = change in transverse dimension (diameter/width) per unit original dimension, $\dfrac{\Delta d}{d}$, occurring perpendicular to the applied longitudinal force.

    Hint: Sideways strain $\Delta d/d$.

26. 26.What is elastic limit?

    The maximum stress (or the upper limit of the deforming force) up to which a body regains its original configuration completely on removal of the load. Beyond it, permanent (plastic) deformation begins.

    Hint: Max stress for full recovery.

27. 27.What is the proportional limit?

    The point on the stress–strain curve up to which stress is directly proportional to strain (Hooke's law is obeyed). It lies at or just below the elastic limit.

    Hint: Hooke's law holds up to here.

28. 28.On a stress–strain curve, what is the yield point?

    The yield point (elastic limit region) is the stress beyond which the material begins to deform plastically — strain increases with little or no increase in stress, and deformation becomes permanent. The stress there is the yield strength.

    Hint: Onset of permanent deformation.

29. 29.What is the breaking (fracture) point?

    The point on the stress–strain curve at which the material actually fractures/breaks. The corresponding stress is the breaking stress; the maximum stress before fracture is the ultimate/tensile strength.

    Hint: Where it snaps.

30. 30.Define ultimate tensile strength.

    The maximum stress a material can withstand before it starts to neck and eventually fracture — the highest point on the stress–strain curve.

    Hint: Peak of the curve.

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