Physics
भौतिक विज्ञान · CEE · MECEE-BL Medical Entrance
0 / 22
chapters done
- Mechanics
-
The syllabus asks for
- Precision, accuracy, significant figures and dimensional analysis
- Scalars and vectors: laws of addition, resolution, scalar and vector products
- Linear motion: equations of motion and their graphical treatment
- Projectile motion, with and without a resistive force
Key points
- Accuracy is closeness to the true value; precision is closeness of repeated readings. Systematic errors spoil accuracy and are not removed by repeating.
- Leading zeros never count as significant; trailing zeros after a decimal point do. Sums keep the fewest decimal places, products the fewest significant figures.
- Percentage errors always add, each multiplied by its power: %(A^pB^q/C^r) = p%A + q%B + r%C.
- Every term in a correct equation has the same dimensions; dimensions convert units and derive power-law relations, but cannot give numerical constants or tell work from torque.
- R^2 = A^2 + B^2 + 2ABcosθ; |A - B| ≤ R ≤ A + B; two equal vectors at 120° have a resultant equal to either.
-
The syllabus asks for
- Newton's laws of motion and the conditions of equilibrium
- Impulse, linear momentum and its conservation
- Work, energy and power; the work–energy theorem; conservation of energy
- Elastic and inelastic collisions
- Solid friction: laws, coefficient, angle of friction and angle of repose
Key points
- Inertia is resistance to change of motion, measured by mass; vec F = dvec p/dt; action and reaction are equal, opposite and act on different bodies, so they never cancel.
- A weighing machine reads m(g ± a) according to the direction of the acceleration; zero in free fall, mg at constant velocity.
- Equilibrium of a rigid body needs zero net force and zero net torque; three concurrent forces in equilibrium obey Lami's theorem.
- Impulse = change in momentum = area under the force–time graph; spreading the same impulse over more time lowers the force.
- With no external force, total momentum is conserved: recoil, explosions, rockets and every collision.
-
The syllabus asks for
- Moment of inertia of a uniform rod and radius of gyration
- Torque, rotational work, kinetic energy and power
- Angular momentum and its conservation
Key points
- Moment of inertia I = Σ mr^2 depends on the mass, its distribution and the axis — not on the angular velocity; it is the rotational analogue of mass.
- Uniform rod: ML^2/12 about the centre, ML^2/3 about an end; the centre gives the least I of all parallel axes (I = Icm + Md^2).
- Radius of gyration k = √I/M: L/(2√3) about the centre and L/√3 about an end; k doubles when I quadruples.
- Torque τ = rFsinθ (unit N m, never joule) and τ = Iα; a force through the axis gives no torque; a couple turns without translating.
- Rotational work τθ, power τω, kinetic energy (1)/(2)Iω^2; rotational equations of motion mirror the linear ones.
-
The syllabus asks for
- Pressure in a fluid; surface tension, surface energy and capillary action
- Viscosity: Newton's law of viscous flow, Stokes' law and terminal velocity, Poiseuille's formula
- Equation of continuity and Bernoulli's principle with applications
Key points
- Pressure in a liquid is P0 + hρ g, the same at one level, independent of the vessel's shape; Pascal's law multiplies force in a hydraulic lift; upthrust equals the weight of fluid displaced.
- Surface tension (N m⁻¹) equals surface energy per unit area (J m⁻²); it falls with temperature and with soap or detergent; a soap film has two surfaces.
- Excess pressure is 2T/r in a drop and 4T/r in a soap bubble — the smaller the bubble, the higher the pressure.
- Capillary rise h = 2Tcosθ/(rρ g): liquids that wet glass (acute angle, concave meniscus) rise; mercury (obtuse, convex) is depressed; a short tube never overflows.
- Viscous force F = η A dv/dx; viscosity of liquids falls and of gases rises on heating; SI unit Pa s.
-
The syllabus asks for
- Angular quantities; centripetal acceleration and force
- Motion in a horizontal and in a vertical circle
- Simple harmonic motion: displacement, velocity, acceleration, restoring force, energy, period and frequency
- Simple pendulum and spring–mass system; forced oscillation and resonance
Key points
- In uniform circular motion speed is constant but velocity is not; the acceleration v^2/r = ω^2r points to the centre, and the centripetal force does no work.
- The centripetal force is supplied by a real force: friction on a level road (vmax = √μ rg), the normal reaction on a banked road (tanθ = v^2/rg), tension, gravity.
- In a vertical circle on a string the least speeds are √gr at the top and √5gr at the bottom; the tension is greatest at the bottom, by 6mg more than at the top.
- SHM: acceleration = -ω^2× displacement; x = Asin(ω t + φ), v = ω√A^2 - x^2; speed is greatest at the mean position, acceleration at the extremes.
- Total energy (1)/(2)mω^2A^2 is constant; KE = PE at x = A/√2; each form of energy oscillates at twice the frequency.
-
The syllabus asks for
- Newton's law of gravitation; acceleration due to gravity and its variation
- Gravitational field strength, potential and potential energy
- Satellites: orbital velocity, period, energy, escape velocity, geostationary orbit
Key points
- Every mass attracts every other with F = Gm1m2/r^2; the force is always attractive, mutual, central and conservative.
- Surface gravity is g = GM/R^2; it belongs to the planet, not to the falling body.
- With height gh = g(R/(R+h))^2 (inverse square); with depth gd = g(1-d/R) (linear, because the outer shell pulls equally all round). g is zero at the centre.
- Rotation reduces g most at the equator: gλ = g - Rω^2cos^2λ; the poles have the largest g and the equator the smallest.
- Field strength GM/r^2 is a vector in N kg⁻¹; potential -GM/r is a scalar in J kg⁻¹, zero at infinity and negative everywhere else.
-
The syllabus asks for
- Stress, strain and Hooke's law
- Young's modulus, bulk modulus and modulus of rigidity; Poisson's ratio
- Elastic potential energy and energy density
Key points
- Elasticity is the recovery of shape after a deforming force is removed; beyond the elastic limit the deformation is plastic and permanent.
- Stress is force per unit area inside the material (Pa); strain is a fractional change of length, volume or angle and has no unit.
- Hooke's law — stress proportional to strain — holds only up to the proportional limit; the constant is the modulus of elasticity.
- Y=(FL)/(AΔ L) applies to stretching and compressing solids. It depends on the material, not on the wire's dimensions; the extension itself obeys Δ L∝ L/d^2.
- K=-(Δ P)/(Δ V/V) applies to every state of matter; for a gas it is P isothermally and γ P adiabatically.
- Heat and Thermodynamics
-
The syllabus asks for
- Thermal energy, heat and temperature; thermal equilibrium and the zeroth law
- Thermometers: liquid-in-glass, resistance and radiation thermometers — principle, advantages and limitations
- Conduction, convection and radiation; black-body radiation and the Stefan–Boltzmann law
Key points
- Temperature measures the average kinetic energy of molecules; thermal energy is the total internal energy (so it depends on mass); heat is energy in transit because of a temperature difference.
- Two bodies in thermal contact reach the same temperature — thermal equilibrium — with no net heat flow. The zeroth law makes "same temperature" transitive and so makes thermometry possible.
- T=θC+273 and θF=(9)/(5)θC+32; the scales agree at −40°; absolute zero is −273.15 °C.
- Liquid-in-glass thermometers read the apparent expansion of the liquid; mercury covers −39 to 357 °C, alcohol −115 to 78 °C.
- Resistance thermometers use R=R0(1+αθ) and are the most accurate over a wide range; thermocouples use the Seebeck emf and are small, fast and wide-ranging; pyrometers measure radiation without contact.
-
The syllabus asks for
- Linear, superficial and cubical expansion and their relation
- Real and apparent expansion of liquids
- Heat capacity, specific heat capacity and the method of mixtures
- Latent heat of fusion and vaporization; the triple point
Key points
- Δ L = LαΔ T, Δ A = AβΔ T, Δ V = VγΔ T, with β = 2α and γ = 3α for an isotropic solid. Area takes 2α, volume takes 3α — never the other way round.
- A hole or a cavity in a heated plate grows by the same fraction as the metal itself; nothing shrinks on heating except water below 4 °C.
- A clamped rod develops σ = YαΔ T, compressive on heating. A pendulum clock runs slow when hot, losing (1)/(2)αΔθ of its time.
- A liquid's real expansion exceeds its apparent expansion by the vessel's: γr = γa + γv. The level in a warmed vessel first dips (the glass grows first) and then rises.
- Water is densest at 4 °C; that is why ice floats, ponds freeze from the top, and pipes burst in a hard frost.
-
The syllabus asks for
- Ideal-gas equation; kinetic theory: pressure, rms speed and energy of molecules
- First law of thermodynamics: isothermal, adiabatic, isochoric and isobaric processes; molar heat capacities
- Second law of thermodynamics: internal-combustion engines, refrigerators and entropy
Key points
- PV = nRT = NkT; R = NAk; P = ρ RT/M. Temperature must be in kelvin, and one mole of any gas occupies 22.4 L at STP.
- Kinetic theory gives P = (1)/(3)ρ crms^2, hence crms = √3RT/M: at the same temperature the lighter gas is faster, and doubling crms needs four times the absolute temperature.
- Average translational kinetic energy is (3)/(2)kT per molecule whatever the gas; the internal energy of an ideal gas depends only on T.
- Degrees of freedom 3, 5, 6 give Cv = (f)/(2)R, Cp = Cv + R and γ = 1.67, 1.40, 1.33. Cp > Cv because the extra heat at constant pressure does work.
- First law: Q = Δ U + W with W done by the gas; Δ U = nCvΔ T in every process.
- Waves and Optics
-
The syllabus asks for
- Progressive waves and the wave equation
- Speed of sound in solids, liquids and gases, and the factors that affect it
- Stationary waves: harmonics and overtones in strings and pipes
- Pressure amplitude, intensity and loudness, pitch and quality
- Doppler effect
Key points
- A progressive wave is y = Asin(ω t - kx), with v = ω/k = fλ; the minus sign means it travels towards +x.
- Particle velocity is vp = -vtimesslope of the profile, with maximum Aω — a completely different number from the wave speed.
- Sound speed is set by stiffness and density: √Y/ρ in solids, √B/ρ in liquids, √γ P/ρ = √γ RT/M in gases. It rises with temperature, falls with molar mass, and does not change with pressure at constant temperature.
- A string fixed at both ends and an open pipe give every harmonic, fn = nv/2L; a closed pipe gives odd harmonics only, fn = (2n-1)v/4L, and has half the fundamental of the open pipe of the same length.
- End correction e = 0.3d per open end; the resonance tube removes it by using l2 - l1 = λ/2.
-
The syllabus asks for
- Reflection at curved mirrors: mirror formula and magnification
- Refraction at plane surfaces, critical angle and total internal reflection; refraction through a prism
- Lenses: lens formula, lens maker's formula, power and combinations
- Dispersion, chromatic aberration and achromatism
Key points
- The Cartesian convention fixes everything: origin at the pole or optical centre, positive along the incident light; a real object has u<0, a concave mirror f<0, a convex lens f>0.
- Mirror: (1)/(v)+(1)/(u)=(1)/(f) and m=-(v)/(u); R = 2f; a convex mirror is always virtual, erect and diminished.
- Refraction: μ = c/v and μ1sin i = μ2sin r; frequency is unchanged at a boundary, wavelength and speed are not.
- Apparent depth = d/μ; a slab shifts the ray sideways without changing its direction; sin C = 1/μ, and TIR needs dense-to-rare plus i>C.
- Prism: A = r1+r2 and δ = i1+i2-A; at minimum deviation the ray is symmetrical and μ = sin((A+δm)/2)/sin(A/2); a thin prism gives δ = (μ-1)A.
-
The syllabus asks for
- Coherent sources and the conditions for interference; Young's double-slit experiment
- Diffraction at a single slit and at a grating; resolving power of optical instruments
- Polarization and Brewster's law
Key points
- Interference is superposition of coherent waves; intensity is I1+I2+2√I1I2cosφ with φ = 2πΔ/λ. Equal sources give 4I0 bright and zero dark.
- Bright fringes need Δ = nλ; dark fringes need Δ = (2n-1)λ/2. Optical path is μ times geometrical path.
- Coherent beams are made by dividing a wavefront (double slit) or an amplitude (thin film). Two independent lamps never interfere.
- Young's double slit: yn = nλ D/d for bright fringes and β = λ D/d for the spacing — independent of the order, proportional to λ and D, inversely proportional to d, and divided by μ in a liquid.
- A slab of thickness t shifts the whole pattern by (μ-1)t/β fringes towards the covered slit without changing β.
- Current Electricity and Magnetism
-
The syllabus asks for
- Ohm's law and Joule's law; resistance, resistivity, emf, potential difference, energy and power
- Resistors in series and parallel; Kirchhoff's laws
- Wheatstone bridge, metre bridge and potentiometer; a galvanometer converted to an ammeter and a voltmeter
- Seebeck and Peltier effects; the thermocouple
Key points
- Current is the rate of flow of charge; I = nAevd with a drift speed of only about 10^-4 m s⁻¹, while the field that drives it travels at nearly light speed.
- Ohm's law V = IR holds for metals at constant temperature; R = ρ L/A, and ρ = m/(ne^2τ) is a property of the material, unchanged by cutting or bending.
- Metals have α > 0 (about 4×10^-3 K⁻¹), semiconductors α < 0, and alloys such as manganin α ≈ 0, which is why they make standard resistors.
- A real cell gives V = E - Ir; the V–I graph has intercept E and slope -r, and the terminal voltage exceeds the emf only while the cell is being charged.
- P = VI = I^2R = V^2/R; use I^2R in series and V^2/R in parallel; 1 kWh = 3.6×10^6 J, and the bill is (power in kW) × (hours) × (rate).
-
The syllabus asks for
- Magnetic field of a straight conductor, a circular coil and a long solenoid
- Force on a moving charge and on a current-carrying conductor; torque on a coil; Hall effect
- Dia-, para- and ferromagnetism: domains, relative permeability, susceptibility and hysteresis
Key points
- A long straight wire gives B=μ0I/2π r, with circular field lines; two parallel wires with currents in the same direction attract, with F/L=μ0I1I2/2π d.
- At the centre of a coil B=μ0NI/2R; on the axis B=μ0NIR^2/2(R^2+x^2)^3/2, which is 0.354 of the centre value at x=R and falls as 1/x^3 far away.
- Inside a long solenoid B=μ0nI is uniform, outside it is nearly zero, and at the ends it is half the interior value.
- The magnetic force F=qvBsinθ is perpendicular to vec v and does no work, so speed and kinetic energy stay constant; r=mv/qB and T=2π m/qB, independent of speed. A velocity component along vec B turns the circle into a helix of pitch v_∥ T.
- A wire feels F=BILsinθ; a coil feels τ=NIABsinθ, maximum when its plane is parallel to the field. A radial field makes a galvanometer's deflection proportional to current.
-
The syllabus asks for
- Faraday's and Lenz's laws; the AC generator, the transformer and eddy currents
- Self and mutual inductance; energy stored in an inductor
- Peak and rms values; impedance, phase, power and Q-factor of LCR circuits
- Rectification with a diode bridge
Key points
- The flux through a coil is Phi=BAcosθ; the emf is the negative rate of change of flux linkage, varepsilon=-N dPhi/dt, and only a changing flux induces one.
- Lenz's law says the induced current opposes the change in flux; that opposition is what makes the law a statement of energy conservation.
- A rod moving across a field has varepsilon=Bvl; the magnetic drag is B^2l^2v/R and the mechanical power you supply equals the I^2R heat produced.
- A coil rotating in a field gives varepsilon=NBAωsinω t; the peak emf is NBAω and it occurs when the flux through the coil is zero.
- A transformer obeys Vs/Vp=Ns/Np=Ip/Is; it needs alternating current, cannot change the frequency, and loses energy to copper, eddy currents, hysteresis and leakage.
- Electrostatics and Capacitors
-
The syllabus asks for
- Electric charge, electrostatic induction and Coulomb's law
- Electric field of point charges; electric potential and potential energy; Gauss's law
- Capacitors: the parallel-plate capacitor, combinations, energy density and the effect of a dielectric
Key points
- Charge is quantised (q = ne), conserved, and additive as a scalar. One coulomb is 6.25×10^18 electronic charges.
- Charging by conduction gives the same sign as the charging body; charging by induction gives the opposite sign, provided the earth is removed before the rod.
- Coulomb's law: F = kq1q2/r^2 in vacuum, divided by K in a medium. Forces superpose as vectors, so the net force is found one charge at a time.
- The null point of two like charges lies between them, nearer the smaller; for equilibrium of three charges the third is opposite in sign and fixed in magnitude.
- Field lines leave positive charge, end on negative charge, never cross, and are perpendicular to conductors. E = 0 inside a conductor, but V is constant there, not zero.
- Modern Physics
-
The syllabus asks for
- Motion of an electron in electric and magnetic fields
- J. J. Thomson's experiment and Millikan's oil-drop experiment
- Photons and the photoelectric effect: laws and Einstein's equation
Key points
- An electron in a field along its velocity is accelerated: eV=(1)/(2)mv^2, so v∝√V.
- In a transverse electric field the path is a parabola, y=eEx^2/(2mv^2); the oscilloscope deflection VdL^2/(4dVa) does not contain e/m, and it falls when the accelerating voltage rises.
- In a magnetic field the path is a circle of radius r=mv/eB, traced at constant speed; the period 2π m/eB is the same for every speed. A velocity component along vec B turns the circle into a helix.
- Thomson used crossed fields: balance gives v=E/B, and the radius in the magnetic field alone gives e/m=E/(B^2r)=1.76×10^11 C kg⁻¹. He measured a ratio, and its constancy proved electrons are in all matter.
- Millikan held a charged drop stationary, so the drag vanished and qE=mg. Every charge was a whole multiple of e=1.60×10^-19 C: charge is quantised.
-
The syllabus asks for
- Bohr's theory of the hydrogen atom: energy levels and spectral series
- de Broglie waves and the uncertainty principle
- X-rays: production, properties and uses; Bragg's law
Key points
- Bohr kept the nuclear atom and added stationary states, mvr = nh/2π, and photon emission on a jump, hf = E2 - E1.
- For hydrogen rn = 0.529n^2 Å, vn = 2.19×10^6/n m s⁻¹ and En = -13.6/n^2 eV; the ground state is bound by 13.6 eV.
- A downward jump n2 → n1 emits 1/λ = R(1/n1^2 - 1/n2^2); each n1 names a series.
- Lyman ends on n = 1 and is ultraviolet; Balmer ends on n = 2 and is the only visible series; Paschen, Brackett and Pfund are infrared.
- The number of lines from level n is n(n-1)/2; lines crowd to a series limit.
-
The syllabus asks for
- The nucleus: charge, size, mass and density; mass defect, binding energy per nucleon and E = mc²
- Nuclear fission and fusion
- Radioactivity: alpha, beta and gamma rays; the decay law, half-life and mean life; carbon dating
- Medical uses of nuclear radiation and its health hazards
Key points
- The nucleus has Z protons and A-Z neutrons; R = R0A^1/3, so volume ∝ A and density is the same for all nuclei (2.3×10^17 kg m⁻³).
- A nucleus is lighter than its parts by Δ m; the missing mass is the binding energy, Eb = Δ m c^2, with 1 u = 931.5 MeV.
- Binding energy per nucleon peaks near iron-56 at 8.8 MeV. Fusion of light nuclei and fission of heavy nuclei both move nuclei up this curve and release energy.
- Fission: a heavy nucleus splits into two mid-mass fragments plus neutrons, releasing about 200 MeV; a chain reaction needs a critical mass.
- Fusion: light nuclei join, releasing energy; it needs about 10^7 K to overcome the Coulomb barrier, and powers the Sun.
-
The syllabus asks for
- Energy bands in metals, semiconductors and insulators; intrinsic and extrinsic semiconductors
- The p–n junction diode, its biasing and its use as a rectifier
- Logic gates: AND, OR, NOT, NAND and NOR
Key points
- In a solid the atomic levels broaden into bands; the valence band is full, the conduction band is where moving electrons live, and the gap between them decides the class of the solid.
- Metals have no gap (or overlapping bands) and their resistance rises with temperature; semiconductors have Eg of about 1 eV and their resistance falls; insulators have Eg>3 eV.
- In an intrinsic semiconductor ne=nh=ni, and conduction is by electron–hole pairs created by thermal energy.
- A pentavalent donor makes an n-type crystal (electrons majority); a trivalent acceptor makes a p-type crystal (holes majority). The crystal stays neutral, and nenh=ni^2.
- At a p–n junction, diffusion and recombination leave a depletion layer of fixed ions and a barrier of 0.7 V (Si) or 0.3 V (Ge).
-
The syllabus asks for
- Particles and antiparticles; leptons and quarks; the Higgs boson
- Nanotechnology
- The Big Bang theory and Hubble's law
Key points
- The Standard Model has six quarks and six leptons, in three generations, each with an antiparticle of the same mass and opposite charge.
- Quarks are confined: only combinations are seen. Baryons are three quarks (p=uud, n=udd); mesons are a quark–antiquark pair (π^+=ubar d).
- The four interactions are strong (gluon), electromagnetic (photon), weak (W, Z) and gravitational (graviton, not yet observed), with strengths in the approximate ratio 1:10^-2:10^-6:10^-38 and ranges from 10^-18 m to infinity.
- The Higgs boson (about 125 GeV/c^2, found at CERN in 2012) is the quantum of the field that gives mass to fundamental particles — not to the photon or gluon, and not most of the mass of a proton.
- Nanotechnology works at 1–100 nm, where the surface-to-volume ratio is large and quantum effects set in; real uses include drug delivery, water treatment, coatings and nanoscale transistors.
No chapter matches. Try another word.
The paper
3 hours, 200 single-best-answer MCQs with four options, 200 marks, 0.25 deducted per wrong answer, merit list from the 50th percentile
| Section | Questions | Marks each | Total |
|---|---|---|---|
| Zoology | 40 | 1 | 40 |
| Botany | 40 | 1 | 40 |
| Chemistry | 50 | 1 | 50 |
| Physics | 50 | 1 | 50 |
| Mental Agility Test | 20 | 1 | 20 |
Where the questions are
Questions each part carries in the paper, out of 50. Area totals follow the official syllabus; where single chapters are shown, the split between them is the NEBians estimate.
- Modern Physics12 Qs
- Mechanics10 Qs
- Current Electricity and Magnetism9 Qs
- Waves and Optics8 Qs
- Heat and Thermodynamics7 Qs
- Electrostatics and Capacitors4 Qs