Properties of Solids and Liquids – JEE Mains Physics

1. Elastic Behaviour and Stress-Strain Relationship

  • Elastic behaviour refers to the ability of a material to return to its original shape after the removal of a deforming force.
  • Stress-Strain Relationship describes how materials deform under applied forces.
  • Formula for Stress (σ) and Strain (ϵ):
    σ = F / A, ϵ = ΔL / L₀
    where F is the force, A is the cross-sectional area, ΔL is the change in length, and L₀ is the original length.

2. Hooke’s Law

  • Hooke’s Law states that the strain in a solid is proportional to the applied stress within the elastic limit.
  • Formula:
    F = kx
    where F is the force, k is the spring constant, and x is the displacement.

3. Young’s Modulus

  • Young’s Modulus (Y) is a measure of the stiffness of a solid material.
  • Formula:
    Y = (Stress / Strain) = (F / A) / (ΔL / L₀) = (FL₀) / (AΔL)

4. Bulk Modulus

  • Bulk Modulus (B) describes the material's response to uniform pressure applied in all directions.
  • Formula:
    B = - (ΔP / ΔV) * V
    where ΔP is the change in pressure, and ΔV is the change in volume.

5. Modulus of Rigidity

  • Modulus of Rigidity (G) is a measure of the material's response to shear stress.
  • Formula:
    G = (Shear Stress / Shear Strain) = (F / A) / (x / L)

6. Pressure Due to a Fluid Column

  • Pressure at a point in a fluid is given by:
    P = ρgh
    where ρ is the fluid density, g is acceleration due to gravity, and h is the height of the fluid column.

7. Pascal’s Law and Its Applications

  • Pascal’s Law states that any change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
  • Applications: Hydraulic presses, car lifts, etc.

8. Viscosity

  • Viscosity is the measure of a fluid’s resistance to flow.
  • Formula for Viscosity (η):
    η = (F * L) / (A * v)
    where F is the force, L is the length, A is the area, and v is the velocity of the fluid flow.

9. Stoke’s Law and Terminal Velocity

  • Stoke’s Law describes the force of viscosity on a spherical object moving through a fluid.
  • Formula:
    F = 6πηrv
    where η is the fluid viscosity, r is the radius of the sphere, and v is the velocity of the sphere.
  • Terminal Velocity is the constant velocity a freely falling object eventually reaches when the resistance of the medium prevents further acceleration.

10. Streamline and Turbulent Flow

  • Streamline Flow: Fluid moves in parallel layers with no disruption between them.
  • Turbulent Flow: Irregular and chaotic flow of fluid with eddies and vortices.
  • Critical Velocity is the velocity at which the flow of the fluid changes from laminar to turbulent.

11. Bernoulli’s Principle and Its Applications

  • Bernoulli’s Principle states that for an incompressible, non-viscous fluid, the total mechanical energy (pressure energy, kinetic energy, and potential energy) remains constant along a streamline.
  • Formula:
    P + ½ρv² + ρgh = constant
  • Applications: Airplane wings, fluid dynamics in pipes, etc.

12. Surface Energy and Surface Tension

  • Surface Tension is the force acting at the surface of a liquid, causing it to behave like a stretched elastic membrane.
  • Surface Energy is the energy required to increase the surface area of a liquid.

13. Angle of Contact and Excess Pressure

  • Angle of contact is the angle formed between the tangent to the surface of the liquid and the solid surface.
  • Excess Pressure across a curved surface:
    P = 2T / r
    where T is the surface tension, and r is the radius of curvature.

14. Applications of Surface Tension

  • Applications include drops, bubbles, and capillary rise.

15. Heat, Temperature, and Thermal Expansion

  • Heat is the energy transferred between bodies at different temperatures.
  • Temperature is a measure of the average kinetic energy of particles in a substance.
  • Thermal Expansion describes the change in the dimensions of a material when heated.

16. Specific Heat Capacity and Calorimetry

  • Specific Heat Capacity (c) is the amount of heat required to change the temperature of 1 kg of a substance by 1°C.
  • Calorimetry is the science of measuring the heat of chemical reactions or physical changes.

17. Change of State and Latent Heat

  • Latent Heat is the heat required to change the state of a substance without changing its temperature.

18. Heat Transfer: Conduction, Convection, and Radiation

  • Conduction: Transfer of heat through a material without the movement of the material itself.
  • Convection: Transfer of heat by the movement of fluids (liquids or gases).
  • Radiation: Transfer of heat through electromagnetic waves.

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