Fundamentals
The core facts every aspirant should own — each a titled nugget with a real-world story, the concept in plain words, and a memory trick. Works even when the internet doesn't.
300 fundamentals
“Astronauts in the ISS float not because there’s no gravity, but because they are in free fall with g ≈ 8.7 m/s².”
g is not zero in orbit; the ISS experiences about 8.7 m/s², but both it and the astronauts are in continuous free fall, giving apparent weightlessness. The trap is equating weightlessness with g = 0.
Memory trick: Weightless ≠ g=0; it's free fall.
“Squeezing a garden hose makes the spray shoot farther because the smaller opening speeds up the water.”
For steady, incompressible flow the volume rate is constant, giving A1 v1 = A2 v2. When the cross-section narrows, the speed must increase to conserve mass. The equation fails for compressible gases at high speed or when there are leaks or unsteady flow.
A1v1 = A2v2
Memory trick: A·v = constant (area × speed).
“When you pull a spring, the force starts at zero and rises linearly, so the average force is half the maximum.”
In the Hooke-law region the stress rises linearly with strain, so the work per unit volume is the area of a triangle, giving ½ σ ε. Omitting the ½ overestimates energy by a factor of two, a frequent error in exams.
Memory trick: Triangle area → ½ base × height
“The low note of a piano and its higher octave are the fundamental and its first overtone.”
Harmonic frequencies fn = n f1 (n = 1,2,3…). Overtones are the frequencies above the fundamental; the 1st overtone is the 2nd harmonic. Students often mix up overtone number with harmonic number.
Memory trick: Overtone # = harmonic # –1
“Heating a sealed balloon makes the air molecules move faster, raising its internal energy.”
Internal energy is the sum of microscopic kinetic energies of all molecules. For an ideal gas it depends only on temperature (U = f/2 nRT). Changing volume or pressure at constant temperature does not change U. Forgetting this leads to wrong ΔU.
Memory trick: U ∝ T only (ideal gas)
“Two rubbed balloons with the same sign of static charge push each other away, showing the force follows the sign of q₁·q₂.”
Coulomb’s law gives magnitude F = k|q₁q₂|/r²; the direction is repulsive if q₁q₂>0 and attractive if q₁q₂<0, along the line joining the charges. Trap: writing only the magnitude and forgetting the sign determines direction.
Memory trick: F ∝ q₁·q₂ → same sign = push, opposite = pull.
“A diode is like a one-way street; it won’t obey V=IR like a straight road.”
Ohm’s law V = IR holds only for ohmic conductors where resistance stays constant with temperature. Devices such as diodes or filament lamps have non-linear V-I characteristics, so V ≠ I·R there. The common mistake is applying Ohm’s law universally without checking linearity.
Memory trick: Ohm = constant R, not universal
“When you quickly turn off a lamp’s coil, the sudden drop in current makes the coil “push back” like a spring resisting compression.”
A changing current in a coil induces an emf ε = –L dI/dt that opposes the change (Lenz’s law). For a solenoid L = μ₀ N² A / l. The induced emf always acts to keep the current at its original value, whether the current is increasing or decreasing.
Memory trick: Lenz’s rule: induced emf always opposes ΔI.
“Reading glasses add +2 dioptres power, meaning focal length 0.5 m (P = 1/f).”
Optical power P (dioptres) is the reciprocal of focal length in metres: P = 1/f. Convex lenses have +P, concave –P. The exam pitfall is inserting f in centimetres directly; always convert f to metres before inverting.
P = 1/f
Memory trick: P (D) = 1 ÷ f (m)
“AND is a two-person password, OR a single-key lock, NOT a light switch that flips on/off.”
Logic gates process binary bits: AND outputs 1 only if both inputs are 1; OR outputs 1 if any input is 1; NOT flips 0↔1. They are built from transistors. Trap: XOR is not just OR; it requires exclusive condition.
Memory trick: AND=all, OR=any, NOT=flip
“Imagine a ruler whose left end marks radio waves and right end gamma rays; the marks get tighter, showing wavelength shrinking as frequency climbs.”
The same spectrum—radio to gamma—must be listed by increasing frequency, not by wavelength in the same direction. As ν rises, λ falls (λ = c/ν) and photon energy rises (E = hν). The frequent mistake is ordering by wavelength as if it followed the same direction as frequency.
Memory trick: Freq ↑ → λ ↓ → photon E ↑
“A car rounding a roundabout at constant speed still feels the road pushing it sideways inward.”
Even with unchanged speed, a body moving on a curved path has a non-zero acceleration because its velocity vector rotates. The magnitude is a = v²/r and points toward the centre of curvature. The frequent mistake is to equate constant speed with zero acceleration; remember direction change also creates acceleration.
Memory trick: Speed steady? Direction turning → acceleration inward.
“A hot cup of tea cools faster in a cold room than in a warm kitchen.”
Newton's law of cooling states that for modest temperature differences and unchanged surroundings, the rate of temperature change is proportional to the excess temperature: dT/dt = -k(T-Ts). The trap: applying it when the surroundings temperature varies or for very large ΔT, where the linear relation fails.
Memory trick: Cooling ∝ ΔT (bigger gap, faster drop).
“A frozen bike wheel spins freely, but its spokes don’t vibrate – similar vibrational modes are ‘frozen’ at low T.”
A trap is to use equipartition at low temperature as if all vibrational modes were active. Vibrations are quantum-frozen until k_BT exceeds their energy spacing, so only translational and rotational modes contribute to C_V. When vibrations turn on, C_V rises and γ falls.
Memory trick: Vibrations count only if kT > hv
“Keeping a battery connected while inserting a dielectric is like inflating a balloon while holding its pressure constant; charge must increase.”
The mistake is to apply the isolated-capacitor reasoning when the capacitor remains connected to a battery. With V fixed, inserting a dielectric lowers the field, the battery supplies extra charge, and C rises by K, giving Q = CV larger. Remember the condition that V is constant.
Memory trick: Battery: V const → Q↑, C↑ (×K).
“A student uses the same iron core for a transformer and a fridge magnet, forgetting that transformer cores need low-loss (narrow loop) material.”
Soft ferromagnets have narrow hysteresis loops, low coercivity and small loss, ideal for transformer cores; hard ferromagnets show wide loops, high coercivity, and retain magnetisation, suited for permanent magnets. Using a hard material in a transformer causes excessive heating. The mistake is assuming one magnetic material fits all applications.
Memory trick: Soft = narrow loop, hard = wide loop.
“A bright spark in a spark plug is often called ionisation, but if the electron only reaches n=5 it’s merely excitation.”
The mistake is labeling every upward transition as ionisation. Only when the electron reaches the continuum (n=∞) does ionisation occur; otherwise the atom remains bound with negative energy. Remember: ionisation = escape to infinity.
Memory trick: Only n=∞ = ionisation.
“When a heavy uranium nucleus splits, the fragments weigh slightly less, and that missing mass powers a nuclear plant.”
Energy is released when the total binding energy of products exceeds that of reactants, i.e., when the final mass is lower. Heavy nuclei release energy by fission; light nuclei (lighter than Fe) release energy by fusion. The trap: assuming any fusion or fission always gives energy.
Memory trick: Go downhill on B/A curve: heavy → fission, light → fusion.
“Measuring 30 cm and 70 cm on a 1 m meter bridge but ignoring the missing 0 cm segment leads to a wrong resistance ratio.”
The balance condition requires the two measured lengths to be parts of the same uniform wire, so l₁ + l₂ must equal the total wire length. Using arbitrary centimetre readings that don’t sum to the wire length violates the derivation and yields an incorrect resistance ratio. Always verify l₁ + l₂ = total before applying R₁/R₂ = l₁/l₂.
Memory trick: Check l₁ + l₂ = total wire, then use R₁/R₂ = l₁/l₂.
“Tightening a guitar string raises its pitch because the wave speed √(T/μ) increases.”
The speed of a transverse wave on a stretched string is v = √(T/μ), with T the uniform tension and μ the linear mass density. Higher tension or lighter string raises v and thus the fundamental frequency. A common error is to use the string’s total mass instead of μ, or to forget the square-root.
v_string = sqrt(T/mu)
Memory trick: v = √(T/μ) – tension over linear density
“Thinking a loop in uniform B has no effect is like believing a windmill won’t spin when wind hits all blades equally.”
Even when the net translational force on a current loop is zero, the opposite forces form a couple, giving torque τ = m × B. The mistake is to equate zero net force with zero rotational motion. Exam trap: ignoring τ in uniform fields.
Memory trick: Couple = opposite forces → spin
“Two ordinary bulbs lighting a room never cast fixed bright-dark bands on the wall.”
Independent light sources are not mutually coherent; their phase relationship changes randomly, so any instantaneous interference washes out over time, leaving no stable pattern. Only sources with a fixed phase relation (e.g., split laser beam) produce observable interference. The myth that any two lights interfere ignores the coherence requirement.
Memory trick: Coherent = fixed phase; random bulbs = no fringes
“A bicycle brake (resistor) gets hot when used, but a flywheel (inductor) only resists speed changes without heating.”
Reactance is not resistance: it depends on frequency and only stores energy, causing a phase shift but no real power loss. Resistance is frequency-independent and converts electrical energy to heat. The common mistake is treating X like R in P = I²R, which overestimates loss.
Memory trick: X stores, R burns
“Reporting the speed as 3.45 m/s when the stopwatch only measured time to the nearest second (2 s) falsely adds precision.”
The mistake is to give more digits than the least-precise measurement allows. Significant figures reflect true uncertainty; any extra digit is meaningless and can mislead. In JEE, always round the final answer to the smallest sig-fig count among the data used.
Memory trick: Round to the weakest measurement’s sig-fig.