# ISC Class 11 Physics Syllabus 2024-25

CISCE has released the Latest Updated Syllabus of the New Academic Session 2024-25, for class 11. It is available under the ‘‘Regulations and Syllabuses’ page of ISC 2026 on www.cisce.org.

Class 11th Syllabus has been released by CISCE. It’s very important for both Teachers and Students to understand the changes and strictly follow the topics covered in each subject under each stream for Class 11th.

We have also updated Oswal Gurukul Books as per the Latest Paper Pattern prescribed by CISCE Board for each Subject Curriculum.

Students can directly access the ISC Physics Syllabus for Class 11 of the academic year 2024-25 by clicking on the link below.

## ISC Physics Class 11 Latest Syllabus 2024-25

There will be two papers in the subject:

Paper I: Theory - 3 hours ... 70 marks

Paper II: Practical - 3 hours ... 15 marks

Project Work … 10 marks

Practical File … 5 marks

Paper I - Theory

70 Marks

 S. NO. UNIT TOTAL WEIGHTAGE 1. Physical World and Measurement 23 Marks 2. Kinematics 3. Laws of Motion 4. Work, Energy and Power 17 Marks 5. Motion of System of Particles and Rigid Body 6. Gravitation 7. Properties of Bulk Matter 20 marks 8. Heat and Thermodynamics 9. Behaviour of Perfect Gases and Kinetic Theory of Gases 10. Oscillations and Waves 10 Marks TOTAL 70 Marks

Note: (i) Unless otherwise specified, only S. I. Units are to be used while teaching and learning, as well as

(ii) All physical quantities to be defined as and when they are introduced along with their units and dimensions.

(iii) Numerical problems are included from all topics except where they are specifically excluded or where only qualitative treatment is required.

1. Physical World and Measurement

Units and Measurements

Measurement: need for measurement; units of measurement; systems of units: fundamental and derived units in SI; measurement of length, mass and time; errors in measurement; significantfigures.

Dimensional formulae of physical quantities and constants, dimensional analysis and its applications.

(a) Importance of measurement in scientific studies; physics is a science of measurement. Unit as a reference
standard of measurement; essential properties. Systems of units; CGS, FPS, MKS, MKSA, and SI; the seven base
units of SI selected by the General Conference of Weights and Measures in 1971 and their definitions, list of
fundamental, supplementary and derived physical quantities; their units and symbols (strictly as per rule); subunits and multiple units using prefixes for powers of 10 (from atto for 10-18 to tera for 1012); other common units such as fermi, angstrom (now outdated), light year, astronomical unit and parsec. A new unit of mass used in atomic physics is unified atomic mass unit with symbol u (not amu); rules for writing the names of units and their symbols in SI (upper case/lower case.) Derived units (with correct symbols); special names wherever applicable; expression in terms of base units (e.g.: N= kg m/s2 ).

(b) Significant figures; their significance; rules for counting the number of significant figures; rules for (a) addition
and subtraction, (b) multiplication/ division; ‘rounding off’ the uncertain digits; order of magnitude as statement of magnitudes in powers of 10; examples from magnitudes of common physical quantities - size, mass, time, etc.

(c) Dimensions of physical quantities; dimensional formula; express derived units in terms of base units
(N = kg m/s2 ); use symbol […] for dimensions of or base unit of; e.g.: dimensional formula of force in terms of
fundamental quantities written as [F] = [MLT–2 ].Principle of homogeneity of dimensions. Expressions in terms of SI base units and dimensional formula may be obtained for all physical quantities as and when new physical quantities are introduced.

(d) Use of dimensional analysis to (i) check the dimensional correctness of a formula/ equation; (ii) to obtain the
dimensional formula of any derived physical quantity including constants; (iii) to convert units from one system to another; limitations of dimensional analysis.

2. Kinematics

(i) Motion in a Straight Line

Frame of references, Motion in a straight line (one dimension): Position-time graph, speed and velocity.

Elementary concepts of differentiation and integration for describing motion, uniform and non- uniform motion, average speed, velocity, average velocity, instantaneous velocity and uniformly accelerated motion, velocity - time and position - time graphs. Relations for uniformly accelerated motion (graphical treatment).

Frame of reference, concept of point mass, rest and motion; distance and displacement, speed and velocity, average speed and average velocity, uniform velocity, instantaneous speed and instantaneous velocity, acceleration, instantaneous acceleration, s-t, v-t and a-t graphs for uniform acceleration and conclusions drawn from these graphs; kinematic equations of motion for objects in uniformly accelerated rectilinear motion derived using graphical, calculus or analytical method, motion of an object under gravity, (one dimensional motion).

Differentiation as rate of change; examples from physics – speed, acceleration, velocity gradient, etc. Formulae for differentiation of simple functions: xn , sinx, cosx, ex and ln x. Simple ideas about integration – mainly. ∫ xn .dx. Both definite and indefinite integrals to be mentioned (elementary calculus not to be evaluated).

(ii) Motion in a Plane

Scalar and Vector quantities with examples. Position and displacement vectors, general vectors and their notations; equality of vectors, addition and subtraction of vectors, Unit vector; resolution of a vector in a plane, rectangular components, Scalar and Vector product of two vectors. Projectile motion and uniform circular motion.

(a) General Vectors and notation, position and displacement vector. Vectors explained using displacement as a prototype - along a straight line (one dimensional), on a plane surface (two dimensional) and in an open space
not confined to a line or a plane (three dimensional); symbol and representation; a scalar quantity, its
representation and unit, equality of vectors. Unit vectors denoted

$$\text{by}\space \hat{i},\hat{j},\hat{k},\space \text{orthogonal unit vectors}\\\text{along x, y and z axes respectively.}\\\text{Examples of one dimensional vector}\\\hat{v}_{1} = a\hat{i}\space \text{or} \space b \hat{j}\text{or\space}\text{c}\hat{k}\\\text{where a, b, c are scalar quantities}\\\text{or numbers;}\\\vec{\text{V}}_{2} = a\hat{i} + b\hat{j}\\\text{is a two dimensional or planar vector,}\\\vec{\text{V}}_{3} = a\hat{i} + b\hat{i} + c\hat{k}$$

is a three dimensional or space vector. Concept of null vector and coplanar vectors.

(b) Addition: use displacement as an example; obtain triangle law of addition; graphical and analytical treatment;
Discuss commutative and associative properties of vector addition (Proof not required). Parallelogram Law; sum and difference; derive expressions for magnitude and direction from parallelogram law; special cases;
subtraction as special case of addition with direction reversed; use of Triangle Law for subtraction also; if

$$\vec{a} + \vec{b} = \vec{c};\\\vec{c} -\vec{a}=\vec{b};$$

In a parallelogram, if one diagonal is the sum, the other diagonal is the difference; addition and subtraction with vectors expressed in terms of unit vectors

$$\hat{i},\hat{j},\hat{k};\space\text{multiplication of a vector}\\\text{by a real number.}$$

(c) Use triangle law of addition to express a vector in terms of its components.

$$\text{If}\space\vec{a} + \vec{b} + \vec{c}\space\\\text{is an addition fact,}\\\vec{c} = \vec{a} + \vec{b}\\\text{is a resolution;}$$

$$\vec{a}\space\text{and}\space\vec{b}\\\text{are components of}\\\vec{\text{c}}.$$

Rectangular components, relation between components, resultant and angle between them. Dot (or scalar)

$$\text{product of vectors}\space\vec{a}.\vec{b} = ab\text{cos}\theta;$$

$$\text{example}\space \text{W} = \vec{\text{F}}.\vec{\text{S}} =\text{FS}\space\text{cos}\space \theta.$$

Special case of θ = 0o , 90o and 1800.

Vector (or cross) product

$$\vec{a}×\vec{b} = \lbrack\text{ab sin}\space \theta\rbrack\hat{n};\\\text{example}: \text{torque}\space \tau = \vec{r}×\vec{\text{F}};\\\text{Special cases using unit vectors}\\\hat{i},\hat{j},\hat{k}\space\text{for}\space \vec{a},\vec{b}\space\text{and}\space \vec{a}×\vec{b}.$$

(d) Various terms related to projectile motion; obtain equations of trajectory, time of flight, maximum height,
horizontal range, instantaneous velocity, [projectile motion on an inclined plane not included]. Examples of projectile motion.

(e) Examples of uniform circular motion: details to be covered in unit 3 (d).

3. Laws of Motion

General concept of force, inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion.

Law of conservation of linear momentum and its applications.

Equilibrium of concurrent forces. Friction: Static and kinetic friction, laws of friction, rolling friction, lubrication.

Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road).

(a) Newton's first law: Statement and explanation; concept of inertia, mass, force; law of inertia; mathematically, if ∑F=0, a=0.

Newton's second law:

$$\vec{\text{p}} = \vec{mv};\space\vec{\text{F}}∝\frac{d\vec{p}}{dt};\\\vec{\text{F}} = k\frac{d\vec{p}}{dt}.\space\\\text{Define unit of force so that k=1;}\\\vec{\text{F}} = \frac{\vec{dp}}{dt};\\\text{ a vector equation.}$$

For classical physics with v not large and mass m remaining constant, obtain

$$\vec{\text{F}} =m\vec{\text{a}}.$$

$$\text{For}\space v\xrightarrow{}c,\space\text{m is not constant. }\\\text{Then}\space m = \frac{m_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}\\\text{Note that F= ma is the special}\\\text{case for classical mechanics.}$$

It is a vector equation.

$$\vec{a}||\vec{F}.$$

Also, this can be resolved into three scalar equations Fx=max etc. Application to numerical problems; introduce tension force, normal reaction force. If a = 0 (body in equilibrium), F= 0. Statement, derivation and explanation of principle of conservation of linear momentum. Impulse of a force: F∆t =∆p.

Newton's third law. Obtain it using Law of Conservation of linear momentum. Proof of Newton’s second law as real law. Systematic solution of problems in mechanics; isolate a part of a system, identify all forces acting on it; draw a free body diagram representing the part as a point and representing all forces by line segments, solve for resultant force which is equal to $$\text{which is equal to}\space m\vec{a}.$$ Simple problems
on “Connected bodies” (not involving two pulleys).

(b) Force diagrams; resultant or net force from Triangle law of Forces, parallelogram law or resolution of forces.

$$\text{Apply net force}\space\Sigma\vec{F} = m\vec{a}$$

Again for equilibrium a=0 and ∑F=0. Conditions of equilibrium of a rigid body under three coplanar forces. Discuss ladder problem.

(c) Friction; classical view and modern view of friction, static friction a self-adjusting force; limiting value; kinetic friction or sliding friction; rolling friction, examples. Laws of friction: Two laws of static friction; (similar) two laws of kinetic friction; coefficient of friction µs = fs(max)/N and µk = fk/N; graphs. Friction as a nonconservative force; motion under friction, net force in Newton’s 2nd law is calculated including fk. Motion along a rough inclined plane – both up and down. Pulling and pushing of a roller. Angle of friction and angle of repose. Lubrication, use of bearings, streamlining, etc.

(d) Angular displacement (θ), angular velocity (ω), angular acceleration (α) and their relations. Concept of centripetal acceleration; obtain an expression for this

$$\text{acceleration using}\space \Delta\vec{v}.$$

Magnitude and direction of

$$\vec{a}\space \text{same as that of}\Delta \vec{v}$$

Centripetal acceleration; the cause of this acceleration is a force - also called centripetal force; the name only indicates its direction, it is not a new type of force, motion in a vertical circle; banking of road and railway track (conical pendulum is excluded).

4. Work, Power and Energy

Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.Potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); Conservative and non-conservative forces.

Concept of collision: elastic and inelastic collisions in one and two dimensions.

$$\text{(Work done)}\space \text{W} = \vec{\text{F}}.\vec{\text{S}} = \text{FScos}\theta.\\\text{If F is variable}\space\text{dW}= \vec{\text{F}}.\vec{\text{dS}}\\\text{and}\space \text{W} = \int dw =\int\vec{\text{F}}.\vec{\text{dS}},\\\text{for}\space \vec{\text{F}}||d\vec{\text{S}}\space \vec{\text{F}}.d\vec{\text{S}} =\text{FdS}\\\text{therefore,}\space\text{W} = \int\text{F.dS}$$

is the area under the F-S graph or if F can be expressed in terms of S,

$$\int\text{F dS}\space\text{can be evaluated.}$$

Example, work done in stretching a spring

$$\text{W} = \int\text{F dx} = \int kx dx\\=\frac{1}{2}kx^{2}.$$

This is also the potential energy stored in the stretched spring

$$\text{U} =\frac{1}{2}kx^{2}.$$

Kinetic energy and its expression, Work-Energy theorem E=W. Law of Conservation of Energy; oscillating spring.
U+K = E = Kmax = Umax (for U = 0 and K = 0 respectively); graph different forms of energy and their transformations. E = mc2 (no derivation).

$$\text{Power\space P} = \frac{W}{t};\text{P} = \vec{\text{F}}.\vec{\text{v}}.$$

(ii) Collision in one dimension; derivation of velocity equation for general case of m1 ≠ m2 and u1 ≠ u2=0; Special cases for m1=m2=m; m1>>m2 or m1<<m2. Oblique collisions i.e. collision in two dimensions.

5. Motion of System of Particles and Rigid Body Idea of centre of mass: centre of mass of a twoparticle system, momentum conservation and centre of mass motion. Centre of mass of a rigid body; centre of mass of a uniformrod.

Moment of a force, torque, angular momentum, laws of conservation of angular momentum and its applications.
Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparative study of linear and rotational motions.

Moment of inertia, radius of gyration, moments of inertia for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications.

Definition of centre of mass (cm), centre of mass (cm) for a two particle system m1x1+m2x2=Mxcm; differentiating, get the equation for vcm and acm; general equation for N particles- many particles system; [need not go into more details];centre of gravity, principle of moment, discuss ladder problem, concept of a rigid body; kinetic energy of a rigid body rotating about a fixed axis in terms of that of the particles of the body; hence, define moment of inertia and radius of gyration; physical significance of moment of inertia; unit and dimension; depends on mass and axis of rotation; it is rotational inertia; equations of rotational motions. Applications: only expression for the moment of inertia, I (about the symmetry axis) of: (i) a ring; (ii) a solid and a hollow cylinder, (iii) a thin rod (iv) a solid and a hollow sphere, (v) a disc - only formulae (no derivations required).

(a) Statements of the parallel and perpendicular axes theorems with illustrations [derivation not required].
Simple examples with change of axis.

(b) Definition of torque (vector);

$$\tau = \vec{r}x\vec{F}\space \text{and angular momentum}\\\vec{\text{L}}\space = \vec{\text{r}}x\vec{\text{p}}\\\text{for a particle (no derivations);}\\\text{differentiate to obtain}\\\frac{d\vec{\text{L}}}{dt} =\tau;$$

similar to Newton’s second law of motion (linear);hence τ =I α and L = Iω; (only scalar equation); Law of conservation of angular momentum; simple applications. Comparison of linear and rotational motions.

6. Gravitation

Kepler's laws of planetary motion, universal law of gravitation. Acceleration due to gravity (g) and its variation with altitude, latitude and depth.

Gravitational potential and gravitational potential energy, escape velocity, orbital velocity of a satellite, Geo-stationary satellites.

(i) Newton's law of universal gravitation; Statement; unit and dimensional formula of universal gravitational constant, G [Cavendish experiment not required]; gravitational acceleration on surface of the earth (g), weight of a body W= mg from F=ma.

(ii) Relation between g and G. Derive the expression for variation of g above and below the surface of the earth; graph; mention variation of g with latitude and rotation, (without derivation).

(iii) Gravitational field, intensity of gravitational field and potential at a point in earth’s gravitational field. Vp = Wαp/m. Derive expression (by integration) for the gravitational potential difference ∆V = VB-VA = G.M(1/rA-1/rB); here Vp = V(r) = -GM/r; negative sign for attractive force field; define gravitational potential energy of a mass m in the earth's field; expression for gravitational potential energy U(r) = Wαp = m.V(r) = -G M m/r; show that ∆U = mgh, for h << R. Relation between intensity and acceleration due to gravity.

(iv) Derive expression for the escape velocity of earth using energy consideration; ve depends on mass of the earth; for moon ve is less as mass of moon is less; consequence - no atmosphere on the moon.

(v) Satellites (both natural (moon) and artificial) in uniform circular motion around the earth; Derive the expression for orbital velocity and time period; note the centripetal acceleration is caused (or centripetal force is provided) by the force of gravity exerted by the earth on the satellite; the acceleration of the satellite is the acceleration due to gravity [g’= g(R/R+h)2 ; F’G = mg’]. Weightlessness; geostationary satellites; conditions for satellite to be geostationary; parking orbit, calculation of its radius and height; basic concept of polar satellites and their uses.

(vi) Kepler's laws of planetary motion: explain the three laws using diagrams. Proof of third law (for circular orbits only).

7. Properties of Bulk Matter

(i) Mechanical Properties of Solids: Elastic behaviour of solids, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, shear modulus of rigidity, Poisson's ratio; elastic energy (qualitative treatment only).

Elasticity in solids, Hooke’s law, Young’s modulus and its determination, bulk modulus and shear modulus of rigidity, work done in stretching a wire and strain energy, Poisson’s ratio.

(ii) Mechanical Properties of Fluids

Pressure due to a fluid column; Pascal's law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure.

Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its
applications.

Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise.

(a) Pressure in a fluid, Pascal’s Law and its applications, buoyancy (Archimedes Principle).

(b) General characteristics of fluid flow; equation of continuity v1a1= v2a2; conditions; applications like use of nozzle at the end of a hose; Bernoulli’s principle (theorem); assumptions - incompressible liquid, streamline (steady) flow, non-viscous and irrotational liquid - ideal liquid; derivation of equation; applications of Bernoulli’s theorem atomizer, dynamic uplift, Venturimeter, Magnus effect etc.

(c) Streamline and turbulent flow - examples; streamlines do not intersect (like electric and magnetic lines of
force); tubes of flow; number of streamlines per unit area α velocity of flow (from equation of continuity v1a1 = v2a2); critical velocity; Reynold's number (significance only) Poiseuille’s formula with numericals.

(d) Viscous drag; Newton's formula for viscosity, co-efficient of viscosity and its units.

Flow of fluids (liquids and gases), laminar flow, internal friction between layers of fluid, between fluid and the
solid with which the fluid is in relative motion; examples; viscous drag is a force of friction; mobile and viscous
liquids.

Velocity gradient dv/dx (space rate of change of velocity); viscous drag F = ηA dv/dx; coefficient of viscosity η = F/A (dv/dx) depends on the nature of the liquid and its temperature; units: Ns/m2 and dyn.s/cm2 = poise.1 poise=0.1 Ns/m2 .

(e) Stoke's law, motion of a sphere falling through a fluid, hollow rigid sphere rising to the surface of a liquid, parachute, obtain the expression of terminal velocity; forces acting; viscous drag, a force proportional to velocity; Stoke’s law; ν-t graph.

(f) Surface tension (molecular theory), drops and bubbles, angle of contact, work done in stretching a surface and surface energy, capillary rise, measurement of surface tension by capillary (uniform bore) rise method.
Excess pressure across a curved surface, application of surface tension for drops and bubbles.

8. Heat and Thermodynamics

(i) Thermal Properties of Matter: Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity, calorimetry; change of state, specific latent heat capacity.

Heat transfer-conduction, convection and radiation, thermal conductivity, qualitative ideas of Blackbody radiation, Wien's displacement Law and Stefan's law.

(a) Temperature and Heat, measurement of temperature (scales and inter conversion). Ideal gas equation and
absolute temperature, thermal expansion in solids, liquids and gases. Specific heat capacity, calorimetry, change of state, latent heat capacity, steady state and temperature gradient. Thermal conductivity; co-efficient of thermal conductivity, Use of good and poor conductors, Searle’s experiment, (Lee’s Disc method is not required). Convection with examples.

(b) Black body is now called ideal or cavity radiator and black body radiation is cavity radiation; Stefan’s law is now known as Stefan Boltzmann law as Boltzmann derived it theoretically. There is multiplicity of technical terms related to thermal radiation - radiant intensity I (T) for total radiant power (energy radiated/second) per unit area of the surface, in W/m2, I (T) =σ T4 ; dimension and SI unit of σ. For practical radiators I =∈. σ T4 where ∈ (dimension less) is called emissivity of the surface material; ∈=1 for ideal radiators.

$$\text{The Spectral radiancy}\space \text{R(λ). I (T)}=\\\int^{\alpha}_{0}\text{R}(\lambda)d\lambda$$

Graph of R(λ) vs λ for different temperatures. Area under the graph is I (T). The λ corresponding to maximum
value of R is called λmax; decreases with increase in temperature.

Wien’s displacement law; Stefan’s law and Newton’s law of cooling. [Deductions from Stefan’s law not necessary].

(ii) Thermodynamics

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics), heat, work and internal energy. First law of thermodynamics, isothermal and adiabatic processes.

Second law of thermodynamics: reversible and irreversible processes.

(a) Thermal equilibrium and zeroth law of thermodynamics: Self explanatory

(b) First law of thermodynamics.

Concept of heat (Q) as the energy that is transferred (due to temperature difference only) and not stored; the
energy that is stored in a body or system as potential and kinetic energy is called internal energy (U). Internal energy is a state property (only elementary ideas) whereas, heat is not; first law is a statement of conservation of energy, when, in general, heat (Q) is transferred to a body (system), internal energy (U) of the system changes and some work W is done by the system; then Q=∆U+W; also W=∫pdV for working substance - an ideal
gas; explain the meaning of symbols (with examples) and sign convention carefully (as used in physics: Q>0 when added to a system, ∆U>0 when U increases or temperature rises, and W>0 when work is done by the system). Special cases for Q=0 (adiabatic), ∆U=0 (isothermal) and W=0 (isochoric).

(c) Isothermal and adiabatic changes in a perfect gas described in terms of PV graphs; PV = constant (Isothermal) and PVγ = constant (adiabatic); joule and calorie relation (derivation of PVγ = constant not required).

Note that 1 cal = 4⋅186 J exactly and J (so-called mechanical equivalent of heat) should not be used in equations. In equations, it is understood that each term as well as the LHS and RHS are in the same units; it could be all joules or all calories.

(d) Derive an expression for work done in isothermal and adiabatic processes; principal and molar heat capacities; Cp and Cv; relation between Cp and Cv (Cp - Cv = R). Work done as area bounded by PV graph.

(e) Second law of thermodynamics, Carnot's cycle. Some practical applications.

Only one statement each in terms of Kelvin’s impossible steam engine and Clausius’ impossible refrigerator. Brief
explanation of the law. Reversible and irreversible processes, Heat engine; Carnot’s cycle - describe realisation
from source and sink of infinite thermal capacity, thermal insulation, etc. Explain using pV graph (isothermal process and adiabatic process) expression and numericals (without derivation) for efficiency η=1-T2/T1.

9. Behaviour of Perfect Gases and Kinetic Theory of Gases

(i) Kinetic Theory: Equation of state of a perfect gas, work done in compressing a gas. Kinetic theory of gases - assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules;
degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number.

(a) Kinetic Theory of gases;

$$\text{p} = \frac{1}{3}\rho\bar{c^{2}}$$

from the assumptions and applying Newton’s laws of motion. The average thermal velocity (rms value)

$$\text{C}_{rms}=\sqrt{\frac{3\rho}{\rho}};$$

calculations for air, hydrogen and their comparison with common speeds. Effect of temperature and pressure on rms speed of gas molecules.

[Note that pV=nRT the ideal gas equation cannot be derived from kinetic theory of ideal gas. Hence, neither can
other gas laws; pV=nRT is an experimental result. Comparing this with $$p =\frac{1}{3}\bar{\text{pc}^{2}}.,$$

from kinetic theory of gases, a kinetic interpretation of temperature can be obtained as explained in the next subunit].

(b) From kinetic theory for an ideal gas (obeying all the assumptions especially no intermolecular attraction and negligibly small size of molecules,

$$\text{we get}\space p = (1/3)p\bar{c}^{2}\\\text{or}\space pV = (1/3)\text{M}\bar{c^{2}}.$$

(No further, as temperature is not a concept of kinetic theory). From experimentally obtained gas laws, we
have the ideal gas equation (obeyed by some gases at low pressure and high temperature) pV = RT for one mole.
Combining these two results (assuming they can be combined),

$$\text{RT}= (1/3)\text{M}\bar{c^{2}} \\= (2/3).\frac{1}{2}\text{M}\bar{c^{2}} =(2/3)K;$$

Hence, kinetic energy of 1 mole of an ideal gas K=(3/2)RT. Average K for 1 molecule = K/N = (3/2) RT/N = (3/2) kT
where k is Boltzmann’s constant. So, temperature T can be interpreted as a measure of the average kinetic energy of the molecules of a gas.

(c) Degrees of freedom and calculation of specific heat capacities for all types of gases. Concept of the law of
equipartition of energy (derivation not required). Concept of mean free path and Avogadro’s number NA.

10. Oscillations and Waves

(i) Oscillations: Periodic motion, time period, frequency, displacement as a function of time, periodic functions. Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring, restoring force and force constant; energy in S.H.M., Kinetic and potential energies; simple pendulum and derivation of expression for its time period.

Simple harmonic motion. Periodic motion, time period T and frequency f, f=1/T; uniform circular motion and its
projection on a diameter defines SHM; displacement, amplitude, phase and epoch, velocity, acceleration, time
period; characteristics of SHM; Relation between linear simple harmonic motion and uniform circular motion. Differential equation of SHM, d2 y/dt22 y=0 from the nature of force acting F=-k y; solution y=A sin (ωt+φ0) where ω2 = k/m; obtain expressions for velocity, acceleration, time period T and frequency f. Graphical representation of displacement, velocity and acceleration. Examples, simple pendulum, a mass m attached to a spring of spring constant k. Derivation of time period of simple harmonic motion of a simple pendulum, mass on a spring (horizontal and vertical oscillations) Kinetic and potential energy at a point in simple harmonic motion. Total energy E = U+K (potential + kinetic) is conserved. Draw graphs of U, K and E Verses y.

(ii) Waves: Wave motion, Transverse and longitudinal waves, speed of wave motion, d isplacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats.

(a) Transverse and longitudinal waves; characteristics of a harmonic wave; graphical representation of a harmonic wave. Distinction between transverse and longitudinal waves; examples; displacement, amplitude, time period, frequency, wavelength, derive v=fλ; graph of displacement with time/position, label time period/wavelength and amplitude, equation of a progressive harmonic (sinusoidal) wave, y = A sin (kx±ωt) where k is a propagation factor and equivalent equations.

(b) Production and propagation of sound as a wave motion; mechanical wave requires a medium; general formula for speed of sound (no derivation). Newton’s formula for speed of sound in air; experimental value; Laplace’s correction; variation of speed v with changes in pressure, density, humidity and temperature. Speed of sound in liquids and solids - brief introduction only. Concept of supersonic and ultrasonic waves.

(c) Principle of superposition of waves; interference (simple ideas only); dependence of combined wave form, on the relative phase of the interfering waves; qualitative only - illustrate with wave representations. Beats (qualitative explanation only); number of beats produced per second = difference in the frequencies of the interfering waves. Standing waves or stationary waves; formation by two identical progressive waves travelling in opposite directions (e.g., along a string, in an air column - incident and reflected waves); obtain y= y1+y2= [2 ym sin (kx)] cos (ωt) using equations of the travelling waves; variation of the amplitude A=2 ymsin (kx) with location (x) of the particle; nodes and antinodes; compare standing waves with progressive waves.

(d) Laws of vibrations of a stretched string. Obtain equation for fundamental

$$\text{frequency f}_o(\frac{1}{2}l)\sqrt{\frac{T}{m}};\\\text{sonometer.}$$

(e) Modes of vibration of strings and air columns (closed and open pipes); standing waves with nodes and antinodes; also in resonance with the periodic force exerted usually by a tuning fork; sketches of various modes of vibration; obtain expressions for fundamental frequency and various harmonics and overtones; mutual relations.

Practical Work-

15 Marks

Given below is a list of required experiments. Teachers may add to this list, keeping in mind the general pattern of questions asked in the annual examinations.

In each experiment, students are expected to record their observations in a tabular form with units at the column head. Students should plot an appropriate graph, work out the necessary calculations and arrive
at the result.

Students are required to have completed all experiments from the given list (excluding demonstration experiments):

1. To measure the diameter of a spherical body using Vernier calipers. Calculate its volume with
appropriate significant figures. Also measure its volume using a graduated cylinder and compare the two.
2. Find the diameter of a wire using a micrometer screw gauge and determine percentage error in cross sectional area.
3. Determine radius of curvature of a spherical surface like watch glass by a spherometer.
4. Equilibrium of three concurrent coplanar forces. To verify the parallelogram law of forces and to
determine weight of a body.
5.  (i) Inclined plane: To find the downward force acting along the inclined plane on a roller due
to gravitational pull of earth and to study its relationship with angle of inclination by plotting graph between force and sin θ.

(ii) Friction: To find the force of limiting friction for a wooden block placed on horizontal surface and to study its relationship with normal reaction. To determine the coefficient of friction.

6. To find the acceleration due to gravity by measuring the variation in time period (T) with effective length (L) of a simple pendulum; plot graphs of T νs √L and T2 νs L. Determine effective length of the seconds pendulum from T2 νs L graph.

7. To find the force constant of a spring and to study variation in time period of oscillation with mass m of a body suspended by the spring. To find acceleration due to gravity by plotting a graph $$\text{of T against}\space \sqrt{m}.$$

8. Boyle's Law: To study the variation in volume with pressure for a sample of air at constant temperature by plotting graphs between p and $$\frac{1}{\text{V}}\space\text{and between p and V.}$$

9. Cooling curve: To study the fall in temperature of a body (like hot water or liquid in calorimeter) with time. Find the slope of the curve at four different temperatures of the hot body and hence, deduce Newton's law of cooling.

10. To study the variation in frequency of air column with length using resonance column apparatus or a long cylindrical vessel and a set of tuning forks.

Hence, determine velocity of sound in air at room temperature.

11. To determine frequency of a tuning fork using a sonometer.

12. To determine specific heat capacity of a solid using a calorimeter.

Demonstration Experiments (The following experiments are to be demonstrated by the teacher):

1. Searle's method to determine Young modulus of elasticity.
2. Capillary rise method to determine surface tension of water.
3. Determination of coefficient of viscosity of a given viscous liquid by terminal velocity method.

Project Work And Practical File –

15 Marks

Project Work – 10 Marks

All candidates will be required to do one project involving some Physics related topic/s, under the guidance and regular supervision of the Physics teacher. Candidates are to prepare a technical report including an abstract, some theoretical discussion, experimental setup, observations with tables of data collected, analysis and discussion of results, deductions, conclusion, etc. (after the draft has been approved by the teacher). The report should be kept simple, but neat and elegant. Teachers may assign or students may choose any one project of their choice.

Suggested Evaluation criteria:

• Title and Abstract (summary)
• Introduction / purpose
• Contents/Presentation
• Analysis/ material aid (graph, data, structure, pie charts, histograms, diagrams, etc.)
• Originality of work