What is the difference between stress and pressure?

While both stress and pressure are defined as force per unit area and share the same SI unit (Pascal), their physical interpretations differ. Pressure is typically an external force acting perpendicularly on a surface, often associated with fluids, and is scalar in nature. Stress, on the other hand, is an internal restoring force developed within a material in response to an external deforming force. It can be normal (perpendicular) or tangential (parallel) to the surface and is a tensor quantity, describing the state of internal forces at a point within a deformable body. In simple terms, pressure is what's applied, stress is what's resisted internally.

Why does water have an anomalous expansion?

Water exhibits anomalous expansion between $0^\circ C$ and $4^\circ C$. Unlike most liquids that expand upon heating, water contracts when heated from $0^\circ C$ to $4^\circ C$, reaching its maximum density at $4^\circ C$. This unique behavior is attributed to the hydrogen bonding between water molecules. At $0^\circ C$, water molecules form an open, cage-like structure (like ice) with relatively large empty spaces. As temperature increases to $4^\circ C$, these hydrogen bonds begin to break, allowing molecules to pack more closely, thus increasing density. Above $4^\circ C$, the kinetic energy of molecules dominates, and normal thermal expansion occurs, causing density to decrease.

How does viscosity affect fluid flow?

Viscosity is a measure of a fluid's resistance to flow, essentially its 'thickness' or internal friction. A highly viscous fluid (like honey) flows slowly because there's significant internal resistance between its layers. A less viscous fluid (like water) flows more easily. In fluid dynamics, viscosity leads to energy dissipation as heat, especially in turbulent flows. It's responsible for the drag force on objects moving through fluids (Stokes' Law) and dictates the flow rate through pipes (Poiseuille's formula). Without viscosity, fluids would flow without any energy loss, which is an idealization.

What is the significance of the angle of contact in surface tension?

The angle of contact ($\theta$) is crucial because it determines whether a liquid will wet a solid surface and how it will behave in capillary action. It's the angle formed between the tangent to the liquid surface and the solid surface, measured inside the liquid. If $\theta 90^\circ$ (e.g., mercury on glass), the liquid does not wet the surface, and capillary action will cause the liquid to fall. If $\theta = 90^\circ$, the liquid surface is flat, and there's no capillary effect. It's a balance between cohesive forces within the liquid and adhesive forces between the liquid and solid.

Explain the concept of terminal velocity.

Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration. When an object falls through a fluid (like air or water), it experiences two main forces: its weight acting downwards and an upward viscous drag force (and possibly buoyant force). As the object accelerates, the drag force increases. Eventually, the drag force (plus buoyancy) becomes equal in magnitude to the object's weight. At this point, the net force on the object is zero, and it stops accelerating, continuing to fall at a constant speed, which is its terminal velocity. This concept is described by Stokes' Law for spherical objects.

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Properties of Bulk Matter

Physics

NEET UG

Version 1Updated 23 Mar 2026

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Properties of Bulk Matter, in the realm of physics, refers to the macroscopic characteristics and behaviors exhibited by materials when considered in large quantities, rather than at the atomic or molecular level. This domain primarily encompasses the study of elasticity in solids, the mechanics of fluids (both liquids and gases) at rest and in motion, and the thermal properties of substances. It …

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Properties of Bulk Matter explores the macroscopic behavior of solids, liquids, and gases. For solids, elasticity is key, describing their ability to regain shape after deformation. Concepts like stress (force per unit area) and strain (fractional deformation) are fundamental, linked by Hooke's Law and various moduli of elasticity (Young's, Bulk, Shear).

Fluids (liquids and gases) are characterized by their ability to flow. Hydrostatics deals with fluids at rest, involving pressure (Pascal's Law) and buoyancy (Archimedes' Principle). Hydrodynamics studies fluids in motion, introducing streamline flow, the equation of continuity, and Bernoulli's Principle.

Viscosity quantifies a fluid's resistance to flow, while surface tension describes the 'skin' effect on liquid surfaces, leading to phenomena like capillarity. Finally, thermal properties cover how matter responds to temperature changes, including thermal expansion (linear, area, volume), specific heat capacity, latent heat for phase changes, and methods of heat transfer (conduction, convection, radiation).

This chapter provides essential principles for understanding material behavior and energy interactions.

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Key Concepts

Young's Modulus and its Application

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Stress —

\sigma = F/A

(Pa)

Strain —

\epsilon = \Delta L/L

(dimensionless)

Hooke's Law —

\sigma = E \epsilon

Young's Modulus —

Y = \frac{\text{Normal Stress}}{\text{Longitudinal Strain}}

Bulk Modulus —

B = \frac{-P}{\Delta V/V}

Shear Modulus —

G = \frac{\text{Tangential Stress}}{\text{Shear Strain}}

Elastic Potential Energy Density —

U = \frac{1}{2} \sigma \epsilon = \frac{1}{2} Y \epsilon^2

Pressure at depth —

P = P_0 + \rho gh

Archimedes' Principle —

F_B = V_{displaced} \rho_{fluid} g

Equation of Continuity —

A_1 v_1 = A_2 v_2

Bernoulli's Principle —

P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}

Stokes' Law (Viscous Drag) —

F_v = 6 \pi \eta r v

Terminal Velocity —

v_t = \frac{2 r^2 g (\rho_{object} - \rho_{fluid})}{9 \eta}

Poiseuille's Formula —

Q = \frac{\pi P r^4}{8 \eta L}

Surface Tension —

T = F/L = \Delta U/\Delta A

Capillary Rise —

h = \frac{2T \cos\theta}{\rho r g}

Excess Pressure (liquid drop) —

\Delta P = \frac{2T}{R}

Excess Pressure (soap bubble) —

\Delta P = \frac{4T}{R}

Linear Expansion —

\Delta L = L_0 \alpha \Delta T

Volume Expansion —

\Delta V = V_0 \gamma \Delta T

(where

\gamma \approx 3\alpha

)

Heat Transfer (Conduction) —

Q/t = -kA \frac{dT}{dx}

Specific Heat Capacity —

Q = mc \Delta T

Latent Heat —

Q = mL

To remember the factors in Terminal Velocity: '2 Raging Densities, 9 Nasty Viscous'

$v_t = \frac{2 \mathbf{R}^2 g (\mathbf{\rho}_{object} - \mathbf{\sigma}_{fluid})}{9 \mathbf{\eta}}$

2 — The numerical factor 2.

Raging — For

R^2

(radius squared).

Densities — For

(\rho - \sigma)

(density difference).

9 — The numerical factor 9.

Nasty Viscous — For

\eta

(coefficient of viscosity).

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