Chapter 7 – Properties of Matter
1. Introduction to Properties of Matter
Matter shows different mechanical properties when forces are applied to it.
The study of deformation of solids and flow of fluids forms an important part of physics.
2. Elasticity
Elasticity is the property of a material by virtue of which it regains its original shape
and size when the deforming force is removed.
Materials like steel are highly elastic, while rubber is less elastic (though it stretches more).
3. Stress
Stress is defined as the internal restoring force per unit area developed inside a body.
$$\text{Stress} = \frac{\text{Force}}{\text{Area}}$$
Types of Stress
- Longitudinal stress
- Shearing stress
- Bulk stress
4. Strain
Strain is the ratio of change in dimension to the original dimension.
$$\text{Strain} = \frac{\Delta L}{L}$$
Strain has no unit and is dimensionless.
5. Stress–Strain Curve
The stress–strain curve explains elastic limit, yield point, ultimate stress, and breaking point.
Hooke’s law is valid only in the linear (elastic) region of the curve.
6. Hooke’s Law
Within elastic limit:
$$\text{Stress} \propto \text{Strain}$$
7. Young’s Modulus
Young’s modulus measures the stiffness of a solid.
$$Y = \frac{\text{Longitudinal stress}}{\text{Longitudinal strain}}$$
8. Bulk Modulus
Bulk modulus measures resistance to change in volume.
$$K = -\frac{\Delta P}{\frac{\Delta V}{V}}$$
Negative sign shows that increase in pressure decreases volume.
9. Modulus of Rigidity (Shear Modulus)
$$\eta = \frac{\text{Shearing stress}}{\text{Shearing strain}}$$
10. Relation Between Elastic Constants
$$Y = 2\eta(1+\nu)$$
$$Y = 3K(1-2\nu)$$
11. Fluids
Fluids are substances that can flow, including liquids and gases.
12. Pressure in Fluids
$$P = \frac{F}{A}$$
Pressure at depth $h$:
$$P = \rho g h$$
13. Buoyancy and Archimedes’ Principle
A body immersed in a fluid experiences an upward force called buoyant force.
$$\text{Upthrust} = \text{Weight of displaced fluid}$$
14. Surface Tension
Surface tension is the force per unit length acting tangentially to the surface.
$$T = \frac{F}{L}$$
SI unit: N/m
15. Excess Pressure in Liquid Drop
$$\Delta P = \frac{2T}{r}$$
Excess Pressure in Soap Bubble
$$\Delta P = \frac{4T}{r}$$
16. Viscosity
Viscosity is the resistance offered by a fluid to the relative motion between its layers.
$$\eta = \frac{F}{A}\frac{dx}{dv}$$
17. Stokes’ Law
$$F = 6\pi \eta r v$$
18. Terminal Velocity
$$v_t = \frac{2r^2(\rho - \sigma)g}{9\eta}$$
19. Effect of Temperature
- Elasticity decreases with increase in temperature
- Viscosity of liquids decreases with temperature
- Viscosity of gases increases with temperature
20. Exam Focus & Common Mistakes
- Do not confuse stress and pressure
- Remember negative sign in bulk modulus
- Surface tension acts tangentially, not normally
- Units and dimensions are frequently tested