Physics
भौतिक विज्ञान · Class 11 · Code 1011 (CDC Phy.101)
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chapters done
- Mechanics
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The syllabus asks for
- Precision and significant figures
- Dimensions and uses of dimensional analysis
Key points
- A measurement is Q = nu, and n1u1 = n2u2; SI has seven base quantities.
- Accuracy = closeness to the true value; precision = closeness of repeated readings, limited by the least count.
- Vernier L.C. = 1 MSD - 1 VSD; screw-gauge L.C. = pitch ÷ number of circular divisions.
- Systematic errors spoil accuracy and are removed by calibration; random errors spoil precision and are reduced by averaging. Quote results as a ± Δ amean.
- Significant figures = certain digits + first uncertain digit. Addition keeps the least decimal places; multiplication keeps the least significant figures.
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The syllabus asks for
- Triangle, parallelogram and polygon laws of vectors
- Resolution of vectors; Unit vectors
- Scalar and vector products
Key points
- Scalars need a magnitude only; vectors need magnitude and direction and add by the triangle, parallelogram or polygon law.
- Parallelogram law: R = √P^2 + Q^2 + 2PQcosθ and tanα = Qsinθ/(P + Qcosθ). Maximum P+Q at 0^°, minimum P-Q at 180^°.
- A closed polygon of vectors means zero resultant — the equilibrium condition.
- Resolution: Ax = Acosθ, Ay = Asinθ; recombine with A = √Ax^2 + Ay^2, tanθ = Ay/Ax.
- A = A/A; A = Axi + Ayj + Azk with A = √Ax^2 + Ay^2 + Az^2 and l^2+m^2+n^2=1.
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The syllabus asks for
- Instantaneous velocity and acceleration
- Relative velocity
- Equation of motion (graphical treatment)
- Motion of a freely falling body
- Projectile motion and its applications
Key points
- Instantaneous velocity is v = dx/dt (slope of the tangent to the x–t graph); acceleration is a = dv/dt = v dv/dx.
- On a v–t graph, slope is acceleration and area is displacement.
- For uniform acceleration: v = u+at, s = ut + (1)/(2)at^2, v^2 = u^2+2as, sn = u + (a)/(2)(2n-1).
- Free fall is uniform acceleration with a = -g (upward positive). Time up equals time down; the landing speed equals the launch speed.
- Projectile motion = uniform horizontal motion + free vertical fall. The path is a parabola, T = 2usinθ/g, H = u^2sin^2θ/2g, R = u^2sin 2θ/g.
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The syllabus asks for
- Linear momentum, Impulse
- Conservation of linear momentum
- Application of Newton's laws
- Moment, torque and equilibrium
- Solid friction: Laws of solid friction and their verifications
Key points
- p = mv (kg m s⁻¹, [MLT^-1]); F = dp/dt, becoming F = ma only for constant mass.
- Impulse J = FΔ t = intFdt = mv - mu, the area under the F–t graph; a longer Δ t means a smaller Fav.
- m1u1 + m2u2 = m1v1 + m2v2: momentum of an isolated system is conserved — recoil, explosions, rocket propulsion.
- Atwood: a = (m1-m2)g/(m1+m2), T = 2m1m2g/(m1+m2); apparent weight in a lift is m(g ± a), zero in free fall.
- Torque τ = rFsinθ = rtimesF (N m); a couple has moment F × d about every point.
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The syllabus asks for
- Work done by a constant force and a variable force
- Power
- Work-energy theorem; Kinetic and potential energy
- Conservation of Energy
- Conservative and non-conservative forces
- Elastic and inelastic collisions
Key points
- Work by a constant force: W = Fscosθ = Fcdots, a scalar in joules. Zero when the force is perpendicular to the displacement.
- Work by a variable force: W = ∫ F dx = area under the F–x graph. For a spring, W = (1)/(2)kx^2.
- Power P = W/t = Fcdotv; 1 hp = 746 W and 1 kW h = 3.6× 10^6 J.
- Work–energy theorem: Wnet = Δ K, with K = (1)/(2)mv^2 = p^2/2m.
- Potential energy: U = mgh (gravitational), U = (1)/(2)kx^2 (elastic).
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The syllabus asks for
- Angular displacement, velocity and acceleration
- Relation between angular and linear velocity and acceleration
- Centripetal acceleration
- Centripetal force
- Conical pendulum
- Motion in a vertical circle
- Applications of banking
Key points
- θ = s/r in radians; ω = dθ/dt = 2π/T = 2π f; α = dω/dt. Angular kinematic equations mirror the linear ones.
- v = rω and at = rα; all points of a rigid rotating body share ω but not v.
- Centripetal acceleration ac = v^2/r = rω^2 = 4π^2r/T^2, directed towards the centre. Total acceleration = √ac^2 + at^2.
- Centripetal force Fc = mv^2/r is supplied by tension, friction, gravity or a component of the normal reaction. Centrifugal force is a fictitious force.
- Conical pendulum: tanθ = v^2/rg, T = mg/cosθ, period Tp = 2π√Lcosθ/g = 2π√h/g.
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The syllabus asks for
- Newton's law of gravitation
- Gravitational field strength
- Gravitational potential; Gravitational potential energy
- Variation in value of 'g' due to altitude and depth
- Centre of mass and centre of gravity
- Motion of a satellite: orbital velocity and time period
- Escape velocity
- Potential and kinetic energy of the satellite
- Geostationary satellite
- GPS
Key points
- Newton's law: F = Gm1m2/r^2 with G = 6.67×10^-11 N m^2 kg^-2; forces are an action–reaction pair, independent of the medium.
- Field strength E = GM/r^2 (a vector, N kg⁻¹); at the surface g = GM/R^2, from which M = gR^2/G.
- Potential V = -GM/r (a scalar, J kg⁻¹) and potential energy U = -GMm/r; E = -dV/dr, and Δ U ≈ mgh near the surface.
- Altitude: gh = g(R/(R+h))^2 ≈ g(1-2h/R). Depth: gd = g(1-d/R), zero at the centre.
- Centre of mass xcm = Σ mixi/Σ mi; it coincides with the centre of gravity only in a uniform field.
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The syllabus asks for
- Hooke's law: Force constant
- Stress, Strain, Elasticity and plasticity
- Elastic modulus: Young modulus, bulk modulus, shear modulus
- Poisson's ratio
- Elastic potential energy
Key points
- Hooke's law: within the elastic limit F = kx, where the force constant k = F/x (N m⁻¹). For a wire k = YA/L, so k depends on shape as well as material.
- Stress = F/A (Pa, [ML^-1T^-2]); strain = change ÷ original value (no unit). Modulus = stress ÷ strain.
- The stress–strain curve runs: proportional limit P, elastic limit E, yield point Y, ultimate stress U, breaking point B. Ductile materials have a long Y–B stretch; brittle ones break just after E.
- Young modulus Y = FL/Ae; bulk modulus B = -pV/Δ V with compressibility K = 1/B; shear modulus η = F/(Aθ) with θ = x/L. Only B applies to liquids and gases.
- Poisson's ratio σ = (Δ d/d)÷(e/L); no unit, theoretical range -1 to 0.5, real materials 0.2–0.4. Also Δ V/V = (1-2σ)e/L.
- Heat and Thermodynamics
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The syllabus asks for
- Molecular concept of thermal energy, heat and temperature; cause and direction of heat flow
- Thermal equilibrium and Zeroth law of thermodynamics
- Thermal equilibrium as working principle of mercury thermometer
Key points
- Internal energy is the total kinetic + potential energy of the molecules; thermal energy is its temperature-dependent (kinetic) part.
- Temperature measures the average molecular kinetic energy: Ek = (3)/(2)kBT with kB = 1.38×10^-23 J K^-1.
- Heat is energy in transit due to a temperature difference. Its cause is the temperature difference and its direction is always hot → cold.
- Thermal equilibrium is the state of zero net heat flow, reached when the two temperatures become equal.
- Zeroth law: if A and B are each in equilibrium with C, they are in equilibrium with each other. This is what makes temperature measurable.
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The syllabus asks for
- Linear expansion and its measurement
- Cubical expansion, superficial expansion and relation with linear expansion
- Liquid Expansion: Absolute and apparent
- Dulong and Petit method of determining expansivity of liquid
Key points
- Linear expansivity α = dfracl2-l1l1Δθ, so l2 = l1(1+αΔθ); unit K⁻¹.
- Pullinger's apparatus measures α: rod in a steam jacket, expansion read on a micrometer screw that completes a bell circuit; α = δ l / (l1Δθ).
- A2 = A1(1+βΔθ) and V2 = V1(1+γΔθ), with β = 2α, γ = 3α and α:β:γ = 1:2:3.
- A cavity or hole expands exactly as if it were filled with the surrounding material.
- A liquid has two expansivities: real γr and apparent γa, with γr = γa + γg where γg = 3αg for the vessel. By the weight thermometer, γa = m/[(M-m)Δθ].
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The syllabus asks for
- Newton's law of cooling
- Measurement of specific heat capacity of solids and liquids
- Change of phases: Latent heat
- Specific latent heat of fusion and vaporization
- Measurement of specific latent heat of fusion and vaporization
- Triple point
Key points
- Heat to change temperature: Q = mcΔθ; heat capacity C = mc; water equivalent W = mc/cw.
- Newton's law of cooling: dQ/dt = -K(θ-θ0), hence θ = θ0 + (θ1-θ0)e^-kt. Valid only for small excess temperature and unchanged surroundings.
- Working form for problems: (θ1-θ2)/t = k[(θ1+θ2)/2 - θ0].
- Specific heat capacity is measured by the method of mixtures, mscs(θs-θ2) = (mwcw+mccc)(θ2-θ1), or electrically, VIt = (mlcl+mccc)Δθ.
- Latent heat is absorbed at constant temperature during a phase change: Q = mL. For water Lf = 3.34×10^5 and Lv = 2.26×10^6 J kg^-1.
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The syllabus asks for
- Conduction: Thermal conductivity and measurement
- Convection
- Radiation: Ideal radiator
- Black-body radiation
- Stefan-Boltzmann law
Key points
- Steady conduction: H = kA(θ1-θ2)/L = -kA dθ/dx; thermal conductivity k is in W m⁻¹ K⁻¹.
- Thermal resistance R = L/(kA); resistances of slabs in series add, and H = Δθ/R.
- Searle's method measures k for good conductors: k = mcw(θ4-θ3)x/[A(θ1-θ2)t]; Lee's disc is used for bad conductors.
- Convection needs a moving fluid; natural convection is driven by density differences, forced convection by a fan or pump. Newton's law of cooling is a convection law.
- Radiation needs no medium. a+r+t=1; a perfect black body has a = e = 1; Kirchhoff's law says good absorbers are good emitters; Prevost's theory says emission never stops.
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The syllabus asks for
- Ideal gas equation
- Molecular properties of matter
- Kinetic-molecular model of an ideal gas
- Derivation of pressure exerted by gas
- Average translational kinetic energy of gas molecule
- Boltzmann constant; root mean square speed
- Heat capacities: gases and solids
Key points
- Gas laws combine into the ideal gas equation pV = nRT = NkT, with R = 8.314 J mol^-1K^-1 and T in kelvin.
- Kinetic theory assumes many identical molecules of negligible volume in random motion, with no forces except during elastic collisions.
- Pressure of an ideal gas: p = (1)/(3)ρoverlinec^2, equivalently pV = (1)/(3)mNoverlinec^2.
- Average translational kinetic energy per molecule is E = (1)/(2)moverlinec^2 = (3)/(2)kT, and per mole (3)/(2)RT — independent of the nature of the gas.
- Boltzmann constant k = R/NA = 1.38×10^-23 J K^-1.
- Waves and Optics
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The syllabus asks for
- Real and Virtual images
- Mirror formula
Key points
- For a spherical mirror the pole P, centre of curvature C and focus F lie on the principal axis, and f = R/2 (derived from the paraxial approximation).
- A real image is formed where reflected rays actually meet; it can be caught on a screen and is inverted. A virtual image is formed where the backward extensions meet; it cannot be caught on a screen and is erect.
- New Cartesian convention: distances from P, positive along the incident light. Concave f<0, convex f>0; real image v<0, virtual image v>0.
- Mirror formula: dfrac1v + dfrac1u = dfrac1f = dfrac2R.
- Magnification: m = dfrachiho = -dfracvu = dfracf-vf = dfracff-u. Negative m = inverted and real; positive m = erect and virtual.
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The syllabus asks for
- Laws of refraction: Refractive index
- Relation between refractive indices
- Lateral shift
- Total internal reflection
Key points
- Laws of refraction: incident ray, refracted ray and normal are coplanar; and dfracsin isin r = 1n2 (Snell's law), usually written n1sin i = n2sin r.
- Absolute refractive index n = c/v; also 1n2 = n2/n1 = v1/v2 = λ1/λ2. Frequency never changes on refraction.
- Reversibility gives 1n2 = 1/2n1, and the chain rule gives 1n2 × 2n3 × 3n1 = 1.
- n = dfracreal depthapparent depth for near-normal viewing; apparent shift = t(1 - 1/n), and layers add: apparent depth = Σ ti/ni.
- A parallel-sided slab leaves the direction unchanged but displaces the ray laterally by d = dfractsin(i-r)cos r, which is zero at normal incidence.
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The syllabus asks for
- Minimum deviation condition
- Relation between angle of prism, minimum deviation and refractive index
- Deviation in small angle prism
Key points
- For a prism of refracting angle A: A = r1 + r2 and δ = i1 + i2 - A.
- The graph of δ against i1 has one minimum. Above the minimum, two angles of incidence give the same deviation; at the minimum they coincide.
- At minimum deviation the passage is symmetrical: i1 = i2, r1 = r2 = A/2, and the internal ray is parallel to the base.
- Prism formula: n = dfracsinleft((A+δm)/(2)right)sinleft((A)/(2)right), with i = dfracA+δm2 at minimum deviation.
- Light can emerge through the second face only if A ≤ 2C, where C is the critical angle; otherwise total internal reflection occurs inside the prism.
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The syllabus asks for
- Spherical lenses, angular magnification
- Lens maker's formula
- Power of a lens
Key points
- Thin lens formula dfrac1v - dfrac1u = dfrac1f with linear magnification m = hi/ho = v/u, in the New Cartesian convention.
- A convex lens gives a real inverted image for any object beyond F1, and a virtual magnified one inside F1; a concave lens always gives a virtual, erect, diminished image.
- Angular magnification M = β/α. For a simple microscope, M = 1 + D/f (image at the near point) and M = D/f (image at infinity), with D = 25 cm.
- Refraction at one spherical surface: dfracn2v - dfracn1u = dfracn2-n1R.
- Lens maker's formula: dfrac1f = (n-1)left(dfrac1R1-dfrac1R2right); in a medium, replace n by nl/nm.
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The syllabus asks for
- Pure spectrum and dispersive power
- Chromatic and spherical aberration
- Achromatism and its applications
Key points
- Dispersion happens because n depends on wavelength, with nV > nR; for a thin prism δ = (n-1)A.
- Angular dispersion θ = (nV-nR)A; mean deviation δY = (nY-1)A.
- Dispersive power ω = dfracnV-nRnY-1 — dimensionless, a property of the material only. Flint glass has roughly twice the ω of crown glass.
- A pure spectrum needs a narrow slit, a parallel incident beam, the prism at minimum deviation, and a lens focusing each colour separately on the screen.
- Chromatic aberration: fV < fR; longitudinal chromatic aberration = ω f. Spherical aberration: marginal rays focus nearer than paraxial rays, leaving a circle of least confusion.
- Electricity and Magnetism
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The syllabus asks for
- Electric charges
- Charging by induction
- Coulomb's law - Force between two point charges
- Force between multiple electric charges
Key points
- Charge is quantised (q = ± ne, e = 1.6×10^-19 C), conserved, additive and independent of speed. Charging transfers electrons only.
- 1 C = 1 A s = 6.25×10^18 electronic charges.
- Charging by induction gives a charge opposite to the inducing charge; the earth connection must be broken before the rod is taken away.
- Coulomb's law: F = dfrac14πvarepsilon0dfracq1q2r^2 with dfrac14πvarepsilon0 = 9×10^9 N m^2C^-2 and varepsilon0 = 8.85×10^-12 C^2N^-1m^-2.
- In a medium the force is reduced: Fmed = Fvac/varepsilonr.
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The syllabus asks for
- Electric field due to point charges; Field lines
- Gauss Law: Electric Flux
- Application of Gauss law: field of a charged sphere, line charge, charged plane conductor
Key points
- E = F/q0, measured in N C⁻¹ = V m⁻¹; for a point charge E = kQ/r^2 with k = 1/4πvarepsilon0 = 9×10^9 SI units.
- Fields superpose vectorially: E = Σ Ei.
- Field lines run from + to -, never cross, are densest where E is largest, meet conductors at right angles and do not exist inside a conductor.
- Electric flux PhiE = EAcosθ, a scalar with unit N m² C⁻¹.
- Gauss's law: oint E· dA = qenc/varepsilon0; only enclosed charge contributes.
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The syllabus asks for
- Potential difference, Potential due to a point charge, potential energy, electron volt
- Equipotential lines and surfaces
- Potential gradient
Key points
- Potential difference VB - VA = WAB/q, in volts (J C⁻¹); absolute potential takes V = 0 at infinity.
- Point charge: V = kQ/r — a scalar that carries the sign of the charge, so potentials add algebraically.
- Potential energy: U = qV; for a pair of charges U = kq1q2/r; for a system add over all pairs.
- 1 eV = 1.6×10^-19 J — a unit of energy, not of potential.
- An equipotential surface has constant V: no work is done moving a charge on it, and it is everywhere perpendicular to the field lines.
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The syllabus asks for
- Capacitance and capacitor
- Parallel plate capacitor
- Combination of capacitors
- Energy of charged capacitor
- Effect of a dielectric: Polarization and displacement
Key points
- C = Q/V, unit farad (C V⁻¹); capacitance depends on geometry and medium only.
- Isolated sphere: C = 4πvarepsilon0R.
- Parallel plate capacitor: E = σ/varepsilon0, V = Ed, and C = varepsilon0varepsilonr A/d. With a partial slab, C = varepsilon0A/(d - t + t/varepsilonr).
- Series: same Q, 1/Ceq = Σ 1/Ci, result smaller than the smallest. Parallel: same V, Ceq = Σ Ci, result larger than the largest.
- Stored energy U = fracQ^22C = (1)/(2)QV = (1)/(2)CV^2; it is the area under the Q–V line.
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The syllabus asks for
- Electric Currents; Drift velocity and its relation with current
- Ohm's law, Electrical Resistance, Resistivity, Conductivity
- Current-voltage relations: Ohmic and Non-Ohmic resistance
- Resistances in series and parallel
- Potential divider
- Electromotive force of a source, internal resistance
- Work and power in electrical circuits
Key points
- Current is I = dQ/dt; in a metal I = nAvde and J = I/A = nevd, with a drift velocity of order 10^-4 m s^-1.
- Ohm's law: V = IR at constant temperature. R = ρ l/A, σ = 1/ρ, and microscopically ρ = m/(ne^2τ).
- Ohmic conductors give a straight I–V line through the origin; lamps, diodes and thermistors are non-ohmic.
- Series: Req = R1+R2+R3. Parallel: 1/Req = 1/R1+1/R2+1/R3.
- Kirchhoff: Σ I = 0 at a junction (charge conservation); Σ E = Σ IR round a loop (energy conservation).
- Modern Physics
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The syllabus asks for
- Nucleus: Discovery of nucleus
- Nuclear density, Mass number, Atomic number
- Atomic mass, Isotopes
- Einstein's mass-energy relation
- Mass defect, packing fraction, BE per nucleon
- Creation and annihilation
- Nuclear fission and fusion; energy released
Key points
- Rutherford's alpha-scattering experiment showed the atom is mostly empty with a tiny, massive, positively charged nucleus of radius about 10^-14 m.
- Z = number of protons, A = number of nucleons, N = A - Z; R = R0A^1/3 with R0 = 1.2 fm, so nuclear density is constant at about 2.3×10^17 kg m^-3.
- 1 u = 1.6605×10^-27 kg = 931.5 MeV. Isotopes have the same Z and different A.
- Mass varies with speed, m = m0/√1-v^2/c^2; from this and dEk = v d(mv) follows Ek = (m-m0)c^2 and hence E = mc^2. A mass defect in u times 931.5 gives the energy in MeV.
- Mass defect Δ m = [Zmp + (A-Z)mn] - M; binding energy B = Δ mc^2; packing fraction f = (M-A)/A.
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The syllabus asks for
- Energy bands in solids (qualitative ideas)
- Difference between metals, insulators and semi-conductors using band theory
- Intrinsic and extrinsic semi-conductors
Key points
- Bringing N atoms together splits each sharp atomic level into N levels so close (sim 10^-29 eV apart) that they form a continuous energy band; between bands lie forbidden gaps.
- The valence band is the highest band filled at 0 K; the conduction band is the empty band above it; their separation is Eg.
- A completely filled band carries no current. Conduction needs empty states just above occupied ones.
- Conductor: bands overlap, Eg = 0. Semiconductor: Eg ≤ 3 eV (Ge 0.7 eV, Si 1.1 eV). Insulator: Eg > 3 eV (diamond 5.47 eV).
- Semiconductors have a negative temperature coefficient of resistance because carrier number grows like e^-Eg/2kT.
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The syllabus asks for
- Particle physics: Particles and antiparticles, Quarks (baryons and mesons), leptons (neutrinos)
- Universe: Big Bang and Hubble law, expansion of the Universe, Dark matter, Black Hole, gravitational wave
Key points
- Every particle has an antiparticle of equal mass and opposite charge. Pair production needs ≥ 1.02 MeV; annihilation of e^-e^+ gives two 0.511 MeV photons.
- Quarks come in six flavours: u, c, t with charge +(2)/(3)e and d, s, b with -(1)/(3)e. Baryons are qqq (p = uud, n = udd); mesons are qq (π^+ = ud). Free quarks are never seen.
- The six leptons are e, μ, τ and their neutrinos. Neutrinos are neutral, feel only the weak force, and oscillate between flavours — proof of tiny mass.
- Hubble's law v = H0 d with H0 ≈ 70 km s^-1Mpc^-1; the Hubble time 1/H0 ≈ 14 billion years.
- Big Bang evidence: the expansion, the 2.725 K cosmic microwave background, and the 75% H / 25% He abundance. Age = 13.8 billion years.
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The paper
3hr, FM 75 written (+25 internal)
| Section | Questions | Marks each | Total |
|---|---|---|---|
| Group A MCQ | 11 | 1 | 11 |
| Group B short | 8 | 5 | 40 |
| Group C long | 3 | 8 | 24 |
Where the hours go
Teaching hours are the board's guide to how much of the paper each part carries.
- Mechanics45 h
- Electricity and Magnetism27 h
- Heat and Thermodynamics26 h
- Waves and Optics15 h
- Modern Physics15 h