WBBSE Madhyamik Physical Science cheat sheet

SI base units used here: length metre (m), mass kilogram (kg), time second (s); speed is m s^-1 and acceleration m s^-2.

Scalars have magnitude only (distance, speed, mass, time); vectors have magnitude and direction (displacement, velocity, acceleration, force).

Average speed = total path length ÷ total time; average velocity = net displacement ÷ total time; average velocity can be zero when speed is not.

For uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as, where u is initial velocity, v final velocity, s displacement.

In a distance–time graph, slope = speed; in a velocity–time graph, slope = acceleration and area under the graph = displacement.

Vernier callipers least count = 1 main-scale division − 1 vernier-scale division; typical value 0.1 mm (0.01 cm).

Screw gauge least count = pitch ÷ number of circular-scale divisions; zero error is added or subtracted with its sign.

For uniform circular motion, speed is constant but velocity changes because direction changes; the motion is therefore accelerated.

Density = mass ÷ volume; relative density is density of substance ÷ density of water at 4 °C, dimensionless.

Newton's first law: a body remains at rest or in uniform motion unless a net external force acts; this property is inertia.

Newton's second law: net force F = ma; acceleration is in the direction of the net force and inversely proportional to mass.

Newton's third law: forces occur in equal and opposite pairs acting on different bodies; they do not cancel on the same body.

Momentum p = mv; impulse = FΔt = change in momentum; both momentum and impulse are vectors.

Weight W = mg; near Earth g ≈ 9.8 m s^-2, so mass 1 kg weighs about 9.8 N.

Work W = Fs cos θ; positive when force has a component along displacement, zero when perpendicular, negative when opposite.

Kinetic energy KE = ½mv²; gravitational potential energy near Earth PE = mgh; work–energy theorem: net work = change in KE.

Power P = work ÷ time = Fv; SI unit watt (W); 1 kW = 1000 W.

In an isolated system with only conservative forces, total mechanical energy (KE + PE) is conserved.

Heat is energy transferred because of temperature difference; temperature is a measure of average kinetic energy of particles.

Kelvin temperature = Celsius temperature + 273 (approximately); SI unit of temperature is kelvin (K).

Specific heat: Q = mcΔT; latent heat: Q = mL, used at constant temperature during change of state.

Thermal expansion: L = L0(1 + αΔT); area expansivity β ≈ 2α; volume expansivity γ ≈ 3α for isotropic solids.

Heat transfer modes: conduction (mainly solids, no bulk motion), convection (fluids, bulk motion), radiation (needs no medium).

Water shows anomalous expansion between 0 °C and 4 °C; it has maximum density at 4 °C, so ice floats on water.

Newton's law of cooling: rate of heat loss ∝ temperature difference from surroundings for small differences.

Calorimetry in an isolated system: heat lost by hotter body = heat gained by colder body, provided no heat loss to surroundings.

Thermal conduction rate through a rod: Q/t = kAΔT/L; k is thermal conductivity, A area, L length.

Wave relation: v = fλ; frequency f in hertz, wavelength λ in metres, speed v in m s^-1.

Sound is a mechanical longitudinal wave; it needs a material medium and cannot travel through vacuum.

Speed of sound in air ≈ 340 m s^-1 at room temperature; it increases with temperature and is generally greater in solids than gases.

Human audible range ≈ 20 Hz to 20 kHz; below 20 Hz is infrasonic, above 20 kHz is ultrasonic.

Echo: total sound path = 2d, so d = vt/2 where t is time between sound and echo.

Pitch depends on frequency; loudness depends on amplitude; quality (timbre) depends on waveform/harmonics.

Sound reflection follows the same angle law as light: angle of incidence equals angle of reflection, with rays and normal coplanar.

Resonance occurs when a body is driven at its natural frequency, producing large-amplitude vibration.

Intensity of sound is power per unit area; it decreases with distance from a point source in open space.

Reflection laws: incident ray, reflected ray and normal are coplanar; angle of incidence = angle of reflection.

Plane mirror image: virtual, erect, same size, laterally inverted; image distance behind mirror equals object distance in front.

Spherical mirror: f = R/2; mirror formula 1/f = 1/v + 1/u with Cartesian sign convention.

Mirror magnification m = h'/h = −v/u; positive m means erect image, negative means inverted.

Refraction: Snell's law n1 sin i = n2 sin r; refractive index n = c/v = real depth/apparent depth.

Total internal reflection occurs from denser to rarer medium when incidence angle exceeds critical angle C; sin C = 1/n.

Lens formula 1/f = 1/v − 1/u with Cartesian sign convention; lens magnification m = v/u.

Power of lens P = 1/f (f in metres); unit dioptre (D); convex lens positive power, concave negative.

Convex lens can form real or virtual images; concave lens always forms virtual, erect, diminished image for a real object.

Ohm's law: V = IR at constant temperature; resistance R = ρL/A, so longer/thinner wires have greater resistance.

Series: same current, R = R1 + R2 + ...; parallel: same voltage, 1/R = 1/R1 + 1/R2 + ...

Electrical power P = VI = I²R = V²/R; energy consumed in kWh = power in kW × time in hours.

Magnetic field around a straight current-carrying conductor consists of concentric circles; right-hand grip rule gives direction.

Fleming's left-hand rule gives force on a current-carrying conductor in a magnetic field (motor effect).

Fleming's right-hand rule gives direction of induced current when a conductor moves in a magnetic field (generator effect).

Faraday's law: changing magnetic flux through a circuit induces emf; Lenz's law says induced current opposes the change in flux.

A current-carrying solenoid behaves like a bar magnet; soft iron inside becomes an electromagnet while current flows.

Domestic wiring uses parallel circuits; fuse and switch are placed in the live wire, and earth wire connects metal casing to earth.

One mole contains 6.022×10²³ particles; molar mass in g mol^-1 is numerically equal to molecular mass in u.

Mole calculations: n = mass ÷ molar mass; n = number of particles ÷ Avogadro number.

At STP (273 K, 1 atm), one mole of ideal gas occupies about 22.4 L; at 273 K and 1 bar it is about 22.7 L.

Boyle's law: PV = constant at constant T; Charles's law: V/T = constant at constant P; Gay-Lussac: P/T = constant at constant V.

Combined gas law: P1V1/T1 = P2V2/T2 for a fixed amount of gas; T must be in kelvin.

Ideal gas equation: PV = nRT; R = 8.314 J mol^-1 K^-1; gas density d = PM/RT.

Dalton's law: total pressure of non-reacting gases = sum of partial pressures.

Balanced chemical equation gives mole ratios; the limiting reactant is completely consumed and determines maximum product.

Percentage composition by mass = (mass of element in one mole ÷ molar mass of compound) × 100.

Atomic number Z = number of protons; mass number A = protons + neutrons; neutral atom has electrons = protons.

Isotopes have same Z but different A (different neutrons); isobars have same A but different Z.

Electron shells fill as 2, 8, 8, 18...; number of valence electrons determines the group for main-group elements.

Modern periodic law: properties of elements are periodic functions of their atomic numbers; the table has 7 periods and 18 groups.

Group 1 = alkali metals, Group 17 = halogens, Group 18 = noble gases; noble gases have stable octet and low reactivity.

Ionic bond: transfer of electrons from metal to non-metal, forming cations and anions held by electrostatic attraction.

Covalent bond: sharing of electron pairs between non-metal atoms; a single bond shares one pair, a double bond two pairs.

Across a period, atomic radius decreases and metallic character decreases; down a group, atomic radius and metallic character increase.

Mendeleev arranged elements by increasing atomic mass and left gaps for undiscovered elements; modern table uses atomic number.

Metals are generally lustrous, malleable, ductile and good conductors; non-metals are usually brittle, dull and poor conductors, except graphite.

Reactivity series: K > Na > Ca > Mg > Al > Zn > Fe > Pb > Cu > Ag > Au; metals above hydrogen displace it from dilute acids.

A more reactive metal displaces a less reactive metal from its salt solution, e.g. zinc displaces copper from copper sulphate.

Electrolysis: electrolyte conducts in molten or aqueous state; oxidation at anode, reduction at cathode; cations move to cathode.

Electrolysis of water: hydrogen at cathode and oxygen at anode, volume ratio 2:1; adding dilute acid increases conductivity.

Electroplating uses the object as cathode, plating metal as anode and a salt of plating metal as electrolyte.

Alkanes: CnH2n+2 (saturated, substitution); alkenes: CnH2n (one C=C, addition); alkynes: CnH2n−2 (one C≡C).

Functional groups: alcohol −OH, aldehyde −CHO, ketone −CO−, carboxylic acid −COOH; these determine characteristic reactions.

Bromine water is decolourised by unsaturated hydrocarbons such as ethene; saturated alkanes do not decolourise it in the dark.