Write the dimensional formula [MᵃLᵇTᶜ] of the quantity, then replace M, L, T with the fundamental units of the target system to obtain the unit directly.

• For work: [W] = [ML²T⁻²], so in CGS the unit is g·cm²/s² (called erg) and in MKS it is kg·m²/s² (called joule).
• The dimensional formula does not change between systems — only the fundamental unit names change. This is why this method works universally.
• Common NEET trap: confusing the dimensional formula itself with the unit — [ML²T⁻²] is a dimension, not a unit. The unit depends on which system's base units you substitute.

Write a formula containing the constant, substitute dimensional formulae of all other quantities, and solve for the constant's dimensions: [G] = [M⁻¹L³T⁻²], [h] = [ML²T⁻¹], [η] = [ML⁻¹T⁻¹].

• For gravitational constant G: from F = Gm₁m₂/r², rearrange to G = Fr²/(m₁m₂), then [G] = [MLT⁻²][L²]/[M][M] = [M⁻¹L³T⁻²].
• For Planck's constant h: from E = hν, [h] = [ML²T⁻²]/[T⁻¹] = [ML²T⁻¹].
• Common NEET trap: using a wrong formula for the constant — if you use F = Gm/r instead of F = Gm₁m₂/r², the dimensions of G come out wrong because you missed a mass term in the denominator.

n₂ = n₁(M₁/M₂)ᵃ(L₁/L₂)ᵇ(T₁/T₂)ᶜ where a, b, c are the dimensional exponents and subscripts 1, 2 denote the known and unknown systems respectively.

• Converting 1 newton to dyne: force has [MLT⁻²], so n₂ = 1 × (kg/g)¹(m/cm)¹(s/s)⁻² = 1 × 10³ × 10² × 1 = 10⁵. Hence 1 N = 10⁵ dyne.
• Converting G from CGS to MKS: G has [M⁻¹L³T⁻²], so n₂ = 6.67 × 10⁻⁸ × (g/kg)⁻¹(cm/m)³(s/s)⁻² = 6.67 × 10⁻⁸ × 10³ × 10⁻⁶ × 1 = 6.67 × 10⁻¹¹ MKS units.
• Common NEET trap: swapping subscripts 1 and 2 — if the known system is CGS (system 1) and unknown is MKS (system 2), M₁ = gram and M₂ = kilogram. Reversing these inverts every ratio and gives an answer off by powers of 10.

The principle of homogeneity states that dimensions of each term on both sides of a physical equation must be identical: if X = A ± (BC)² ± √(DEF), then [X] = [A] = [(BC)²] = [√(DEF)].

• A dimensionally correct equation may or may not be physically correct — for example, s = ut − ½at² is dimensionally correct ([L] = [L] on each term) but physically wrong (the correct sign is s = ut + ½at²).
• Dimensionless constants (π, ½, 2) do not affect dimensional checks — they contribute [M⁰L⁰T⁰] and can be ignored during the verification.
• Common NEET trap: concluding that a dimensionally correct equation must be physically correct — NEET specifically exploits this by offering a formula with correct dimensions but wrong numerical coefficients or signs.

If a physical quantity depends on other quantities as a product-type function, assume the relation Q = K·p^x·q^y·r^z and equate dimensions on both sides to find x, y, z. K is a dimensionless constant that cannot be determined.

• For simple pendulum: T = Kmˣlʸgᶻ gives [T] = [Mˣ][Lʸ][LT⁻²]ᶻ = [MˣLʸ⁺ᶻT⁻²ᶻ]. Equating: x = 0, y + z = 0, −2z = 1, solving: z = −½, y = ½, so T = K√(l/g).
• For Stoke's law: F = K·ηˣ·rʸ·vᶻ gives [MLT⁻²] = [ML⁻¹T⁻¹]ˣ[Lʸ][LT⁻¹]ᶻ. Equating M, L, T gives x = 1, y = 1, z = 1, hence F = Kηrv (experimentally K = 6π).
• Key limitation: dimensional analysis cannot determine dimensionless constants, fails for sums/differences of variables, and cannot handle transcendental functions (sin, cos, log, exponential) — NEET tests these limitations directly.