Physics — Class 11 (CBSE)

Board: CBSE | Class: 11 | Subject: Physics (NCERT Part I & II) Class 11 Physics marks the transition from descriptive science to mathematical physics. Strong conceptual clarity here is essential for Class 12, JEE, and NEET.

Overview

Class 11 Physics covers mechanics (kinematics, dynamics, rotation), properties of matter, thermodynamics, oscillations, and waves. The syllabus is divided into two parts across two NCERT textbooks.

Exam Pattern: Theory — 70 marks | Practical — 30 marks | Total — 100 marks

Physical World and Measurement

Fundamental and Derived Units

SI Base Units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd)
All other units are derived from these seven base units

Dimensional Analysis

Every physical quantity has dimensions: [M], [L], [T], [A], [K], [mol], [cd]
Uses: Checking equation correctness; deriving relationships; converting units
Limitation: Cannot determine dimensionless constants; cannot distinguish same-dimensional quantities

Significant Figures and Errors

Absolute error = |measured value − true value|
Relative error = absolute error / true value
Percentage error = relative error × 100%
Rules: all non-zero digits significant; zeros between significant digits are significant; trailing zeros after decimal are significant

Kinematics

Motion in a Straight Line

Position, displacement, velocity, acceleration — all vectors (except distance and speed)
Uniformly accelerated motion — equations of motion:

v = u + at
s = ut + ½at²
v² = u² + 2as
sₙ = u + a(2n-1)/2   [displacement in nth second]

Motion in a Plane

Projectile motion: Horizontal — uniform velocity; Vertical — uniform acceleration (g)

Range R = u²sin2θ/g
Maximum height H = u²sin²θ/2g
Time of flight T = 2u sinθ/g

Maximum range when θ = 45°
Uniform Circular Motion:
Centripetal acceleration: a = v²/r = ω²r
Centripetal force: F = mv²/r (directed towards centre)

Relative Velocity

v_AB = v_A - v_B — velocity of A relative to B

Laws of Motion

Newton's Laws

First Law: Inertia — objects resist change in state of motion
Second Law: F = dp/dt = ma (net external force)
Third Law: Action-reaction — equal, opposite, on different objects

Friction

Type	Description
Static friction	Opposing force before motion; `f_s ≤ μ_s N`
Kinetic friction	During motion; `f_k = μ_k N` (μ_k < μ_s)
Rolling friction	Least resistance

Circular Motion Dynamics

Banking of roads: tan θ = v²/rg (ideal, no friction)
Vertical circular motion: Minimum speed at top of loop: v_min = √(gr)

Work, Energy and Power

Work-Energy Theorem

W_net = ΔKE = ½mv² - ½mu²

Conservative and Non-Conservative Forces

Conservative: Work done independent of path; potential energy defined (gravity, spring, electrostatic)
Non-conservative: Work depends on path (friction)

Elastic and Inelastic Collisions

Type	KE conserved?	Momentum conserved?
Perfectly elastic	Yes	Yes
Inelastic	No	Yes
Perfectly inelastic	No (max loss)	Yes

For elastic collision (1D):

v₁ = (m₁-m₂)u₁/(m₁+m₂) + 2m₂u₂/(m₁+m₂)
v₂ = 2m₁u₁/(m₁+m₂) + (m₂-m₁)u₂/(m₁+m₂)

System of Particles and Rotational Motion

Centre of Mass

x_cm = (m₁x₁ + m₂x₂)/( m₁ + m₂)

For uniform bodies: CM at geometric centre
Velocity of CM = (m₁v₁ + m₂v₂)/(m₁+m₂)

Rotational Kinematics

Analogous to linear kinematics: | Linear | Rotational | |---|---| | x | θ | | v | ω | | a | α | | m | I (moment of inertia) | | F | τ (torque) | | p = mv | L = Iω |

τ = Iα    (analogous to F = ma)
L = Iω    (angular momentum)

Moment of Inertia

Body	Axis	I
Solid sphere	Diameter	2/5 mr²
Hollow sphere	Diameter	2/3 mr²
Solid cylinder/disk	Own axis	½mr²
Rod	Centre, perpendicular	mL²/12

Theorems: - Parallel axis: I = I_cm + Md² - Perpendicular axis: I_z = I_x + I_y (for laminar bodies)

Rolling Motion

KE_total = ½mv² + ½Iω² = ½mv²(1 + k²/r²)

where k = radius of gyration

Gravitation

Newton's Universal Law

F = Gm₁m₂/r²    G = 6.674 × 10⁻¹¹ N·m²/kg²

Gravitational Field and Potential

g = GM/R² at surface
g decreases with altitude and depth
g is maximum at poles; minimum at equator

Escape Velocity and Orbital Velocity

Escape velocity: v_e = √(2GM/R) = √(2gR) ≈ 11.2 km/s
Orbital velocity: v_o = √(GM/r) = √(gR²/r)

Note: v_e = √2 × v_o (at Earth's surface)

Kepler's Laws

Law of Orbits: All planets move in elliptical orbits with Sun at one focus
Law of Areas: Equal areas swept in equal times (conservation of angular momentum)
Law of Periods: T² ∝ a³ (a = semi-major axis)

Properties of Bulk Matter

Elasticity

Stress = Force/Area (Pa); Strain = Change/Original (dimensionless)
Young's Modulus (Y) = Longitudinal stress/strain (for stretching/compression)
Bulk Modulus (K) = Volumetric stress/strain (for fluids)
Shear Modulus (G) = Shear stress/strain

Fluid Statics

Pascal's Law: Pressure applied to enclosed fluid is transmitted equally in all directions
Hydraulic lift: F₂ = F₁ × A₂/A₁
Pressure at depth h: P = P₀ + ρgh
Archimedes' Principle: Buoyant force = weight of displaced fluid

Fluid Dynamics

Equation of continuity: A₁v₁ = A₂v₂ (conservation of mass)
Bernoulli's Theorem: P + ½ρv² + ρgh = constant (conservation of energy for ideal fluid)
Applications: Venturimeter, aircraft lift, Bunsen burner, spray gun

Surface Tension and Viscosity

Surface tension (T): F = TL; excess pressure inside bubble = 4T/r; inside drop = 2T/r
Capillarity: h = 2T cosθ/ρgr
Viscosity (η): F = ηA(dv/dx); Stokes' law: F = 6πηrv
Reynolds number: Re = ρvD/η; turbulence when Re > 3000

Thermodynamics

Zeroth Law

Objects in thermal equilibrium with a third object are in thermal equilibrium with each other. (Basis of thermometers)

First Law

ΔU = Q - W

Heat added to system = Increase in internal energy + Work done by system

Thermodynamic Processes

Process	Condition	Q-W relation
Isothermal	T = const	ΔU = 0; Q = W
Adiabatic	Q = 0	ΔU = -W
Isochoric	V = const	W = 0; ΔU = Q
Isobaric	P = const	All terms non-zero

Second Law

Kelvin-Planck: No engine can convert heat entirely to work in a cycle
Clausius: Heat cannot spontaneously flow from cold to hot body

Carnot Engine

η = 1 - T₂/T₁ = 1 - Q₂/Q₁

Maximum possible efficiency for heat engine operating between T₁ (hot) and T₂ (cold).

Kinetic Theory of Gases

PV = nRT (ideal gas equation)
Average KE per molecule = 3/2 kT where k = Boltzmann constant
RMS speed = √(3RT/M) = √(3kT/m)
Degrees of freedom: monoatomic = 3; diatomic = 5; polyatomic = 6

Specific heats: Cₚ - Cᵥ = R | γ = Cₚ/Cᵥ - Monoatomic: γ = 5/3; Diatomic: γ = 7/5

Oscillations and Waves

Simple Harmonic Motion (SHM)

SHM condition: restoring force ∝ −displacement: F = −kx

x = A sin(ωt + φ)
v = Aω cos(ωt + φ)
a = −ω²x
ω = √(k/m)     T = 2π√(m/k)

Energy in SHM:

KE = ½mω²(A² - x²)
PE = ½mω²x²
Total E = ½mω²A² = constant

System	Time Period
Simple pendulum	T = 2π√(L/g)
Spring-mass	T = 2π√(m/k)

Waves

Transverse waves: Displacement ⊥ propagation (light, string waves)
Longitudinal waves: Displacement ∥ propagation (sound)

v = fλ = ω/k
y = A sin(kx - ωt)     [progressive wave]

Speed of sound in medium: v = √(B/ρ) (B = bulk modulus) Newton's formula corrected by Laplace: v = √(γP/ρ) → 332 m/s at 0°C

Stationary waves: formed by superposition of two identical waves in opposite directions

y = 2A sin(kx) cos(ωt)

Nodes — zero amplitude (sin kx = 0)
Antinodes — maximum amplitude (sin kx = ±1)

Doppler Effect:

f' = f × (v ± v_o)/(v ∓ v_s)

(+ when moving towards, − when moving away)

Important Constants

Constant	Value
G	6.674 × 10⁻¹¹ N·m²/kg²
g	9.8 m/s²
R (gas constant)	8.314 J/mol·K
k (Boltzmann)	1.38 × 10⁻²³ J/K
Speed of sound (air, 0°C)	332 m/s
Speed of light	3 × 10⁸ m/s