Revision: Properties of Bulk Matter Physics (Theory) ISC (Science) ISC Class 11 CISCE

A body that regains its original shape and size completely and instantaneously upon removal of the deforming force is said to be perfectly elastic.

If a body regains its original shape and size after removal of the deforming force, it is called an elastic body and the property is called elasticity.

The permanent deformation in substances (like putty and mud) that do not return to their original shape after the deforming force is removed is called plastic deformation (or plasticity).

When a solid is deformed and returns to its original shape upon removal of the force, the deformation is called elastic deformation.

A body that regains its original shape and size after removal of the deforming force is called an elastic body, and the property is called elasticity.

OR

The property by which a body returns to its original shape after the removal of a deforming force is called elasticity.

A body that does not regain its original shape and size and retains its altered shape or size upon removal of the deforming force is called a plastic body, and the property is called plasticity.

The strain is defined as the ratio of change in dimensions of the body to its original dimensions.

Strain = `"change in dimensions"/"original dimensions"`

The ratio of change in volume of the body to its original volume is called volume strain: ΔV/V.

The internal restoring force per unit area of a body is called stress.

OR

The internal restoring force acting per unit area of a deformed body is called stress.

• SI Unit: N/m² (pascal, Pa)
   Dimensions: [M¹L⁻¹T⁻²]

Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.

OR

The ratio of change in configuration to the original configuration is called strain.

• It has no unit and no dimensions (pure ratio).

The ratio of change in length of the body to its initial length is called longitudinal strain: ε = ΔL/L.

The angular displacement of the surface in direct contact with the applied shear stress from its original position is called shear strain: τ = W/L = tan ⁡θ.

When there is an increase in the length or extension of the body in the direction of the applied force, the stress produced is called tensile stress.

When there is a decrease in the length or compression of the body due to the applied force, the stress produced is called compressive stress.

When equal normal forces are applied on every surface of a body causing a change in volume, the restoring force opposing this change per unit area is called hydraulic stress (also called volume stress).

The modulus of elasticity of a material is the ratio of stress to the corresponding strain. It is defined as the slope of the stress-strain curve in the elastic deforming region and depends on the nature of the material.

\[\frac {stress}{strain}\] = Constant

The constant is called the modulus of elasticity.

OR

The constant ratio of stress to strain within the elastic limit is called the Modulus of Elasticity.

"Shear modulus or modulus of rigidity: It is defined as the ratio of shear stress to shear strain within elastic limits."

OR

The ratio of shearing stress to the corresponding shearing strain in a material is called the Shear Modulus or Modulus of Rigidity, denoted by G.

The thrust (Normal Force) exerted by a liquid at rest on unit area of the surface in contact is called pressure.

P = \[\frac {F_⊥_​​}{A}\]

• SI Unit: pascal (Pa) = 1 Nm⁻²
  Dimensions: [ML⁻¹T⁻²]

The difference between the hydrostatic pressure (P) and the atmospheric pressure (P₀), measured by a manometer, is called gauge pressure: P − P₀ = ρgh

The weight per unit volume of a substance is called specific weight or weight density: W = mg/V

• SI Unit: N/m³

The ratio of the density of a given fluid to the density of pure water at 4°C is called relative density. It is a unitless quantity.

The force which produces compression is called thrust. Its S.I unit is the newton.

The mass per unit volume of a substance is called density: ρ = M/V

• SI Unit: kg/m³, Dimensions: [ML⁻³T⁰] 

SI unit of pressure is the pascal (Pa) or Nm⁻²
One Pascal: When a force of one newton acts normally on an area of one square metre (1 m²) then the pressure acting on the surface acting on the surface is called one Pascal.

The maximum constant velocity acquired by a body while falling freely through a viscous medium is called the terminal velocity V_T.

The property of a fluid by virtue of which it opposes the relative motion between its different layers, with the force that comes into play, is called viscosity; and that force is called the viscous force.

where η is the coefficient of viscosity.

The coefficient of viscosity of a liquid is defined as the viscous force acting tangentially per unit area of a liquid layer having a unit velocity gradient in a direction perpendicular to the direction of flow of the liquid.

The rate of change of velocity (dv) with distance (dx) measured from a stationary layer is called velocity gradient.

∴ Velocity gradient = `(dv)/dx`

The constant maximum velocity acquired by a body while falling through a viscous fluid is called terminal velocity.

When a liquid flows such that particles passing through a given point have different velocities from the predecessor, such a flow is called turbulent flow.

When a liquid flows such that each particle passing through a specific point follows the exact same path at the same speed as the particle before it, this type of flow is called streamline flow or steady flow.

The limiting velocity up to which flow is streamline and beyond which it changes to turbulent is called critical velocity.

v_C​ = (R_e ​× η)/(ρl)

Surface tension is defined as the force per unit length acting at right angles to an imaginary line drawn on the free surface of the liquid. 

When a liquid is in contact with a solid, the angle between the tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called the angle of contact.

The angle between tangents drawn at the point of contact to the liquid surface and the solid surface inside the liquid is called the angle of contact for a pair of solid and liquid. It is denoted by θ.

Surface tension is defined as the force acting on a unit length of an imaginary line drawn on the free surface of the liquid, the direction of the force being perpendicular to the line so drawn and acting parallel to the surface.

The formula for modulus of rigidity is:

η = \[\frac{\text{Shear Stress}}{\text{Shear Strain}}=\frac{F/A}{\theta}=\frac{F}{A\cdot\theta}\]

Where:

• η = Modulus of rigidity (Pa or N/m²)
• F = Tangential force applied (N)
• A = Cross-sectional area on which force acts (m²)
• θ = Shear strain = Δl/l (in radians)
• Δl = Displacement of the upper surface relative to the lower surface (m)
• l = Original height of the block (m)

SI Unit: Pascal (Pa) or N/m²​

Dimensional Formula: M¹L⁻¹T⁻²

v = \[\frac{2}{9}\cdot\frac{r^2(\rho-\sigma)g}{\eta}\]

where:

• v = terminal velocity
• r = radius of the body
• ρ = density of the body
• σ = density of the fluid
• g = acceleration due to gravity
• η = coefficient of viscosity of the fluid

Hooke's Law was discovered by English scientist Robert Hooke in 1660. He first stated it as a Latin anagram: "As the extension, so the force."

Statement: For small deformations, stress is directly proportional to strain, within the elastic limit.

Key Points:

• Hooke's Law is a measure of elasticity.
• It is valid only up to the elastic limit. Beyond this, the material does not return to its original shape and Hooke's Law no longer applies.
• In springs: The force needed to extend or compress a spring by distance x is proportional to that distance → F = −kx (where k is the spring constant).
• Hooke's Law is applicable only in the case of elastic deformation.

Statement: Pascal's Law states that when pressure is applied to a confined (enclosed) fluid, it is transmitted undiminished and equally in all directions throughout the fluid and to the walls of its container.

Mathematical Expression:

Key Points:

• Pressure changes by the same value at every point inside an incompressible, confined liquid.
• Used in hydraulic machines where a small force on a small area produces a large force on a large area.
• Applications: Hydraulic lift, hydraulic brake, hydraulic press, hydraulic jack.

(b) There is no gravitational force acting downwards. However, when the starting velocity is 20 m/s, the viscous force, which is directly proportional to velocity, becomes maximum and tends to accelerate the ball upwards.

\[\text{ When the ball falls under gravity, }\]

\[\text{ neglecting the density of air: } \]

\[\text{ Mass of the sphere = m }\]

\[\text{ Radius = r }\]

\[\text{ Viscous drag coeff . }= \eta\]

\[\text{Terminal velocity is given by}: \]

\[\text{ mg  }= 6\pi\eta r v_T \]

\[ \Rightarrow \frac{6\pi\eta r v_T}{m} = g . . . (1)\]

\[\text{ Now, at terminal velocity, the acceleration of the ball due to the viscous force is given by: } \]

\[a = \frac{6\pi\eta r v_T}{m}\]

\[\text{ Comparing equations (1) and (2), we find that : } \]

\[ \text{ a = g }\]

Thus, we see that the initial acceleration of the ball will be 9.8 ms - 2  .

(c) The velocity of the ball will decrease with time because of the upward viscous drag. As the force of viscosity is directly proportional to the velocity of the ball, the acceleration due to the viscous force will also decrease.

(d) When all the kinetic energy of the ball is radiated as heat due to the viscous force, the ball comes to rest. 

• Hydraulic Press — Two cylinders (C & D) filled with liquid; small force applied on piston P₁ (smaller area A₁) is converted into a very large upward force on piston P₂ (larger area A₂), since A₂ > A₁.
• Hydraulic Lift — Works on Pascal's Law to lift or support heavy objects such as cars and trucks using liquid pressure.
• Hydraulic Brakes — Small force on the brake pedal is instantly transmitted equally through brake fluid to all cylinders, producing a large thrust on the wheels to stop the vehicle.

• Flow is streamline when velocity is low (parallel, orderly layers).
• Flow turns turbulent when velocity exceeds critical velocity (disordered, mixing layers).
• At low velocity → dye filament stays parallel in pipe (laminar).
• At high velocity → dye filament breaks and spreads (turbulent).

• Aerofoil / Airplane Wing: Air moves faster over the curved top surface → lower pressure above, higher below → upward dynamic lift.
• Spray / Atomizer: High-speed air over a tube creates low pressure → liquid rises and is expelled as droplets.
• Blowing off Roofs: High-velocity wind above roof creates low pressure → atmospheric pressure inside lifts the roof off.
• Magnus Effect (Spinning Ball): A spinning ball drags air, creating pressure difference between upper and lower sides → ball moves in a curved path.
• Venturimeter: Used to measure flow rate of liquid through pipes using pressure difference between wide and narrow sections.
• Attraction between Two Boats: Water between boats moves faster → pressure decreases → boats are pulled toward each other.

• A highly soluble impurity increases surface tension, while a partially soluble impurity (e.g., detergent) decreases it; a waterproofing agent increases it.
• Surface tension decreases with increase in temperature, given by T = T₀(1 − αθ), where T₀​ is surface tension at 0°C and α is the temperature coefficient.
• When a soap bubble is charged (positively or negatively), force acts outward on the surface, increasing its radius — thus electrification always decreases surface tension.