Convert 1 N/m into dyne/cm using dimensional analysis

Step by step

1. The dimension of surface tensionSurface tension has the dimensions [M T⁻²]. Only the powers of M, L and T matter for the conversion.
2. The conversion ruleA quantity with dimensions [M^a L^b T^c] has the number n₂ = n₁ [M₁/M₂]ᵃ [L₁/L₂]ᵇ [T₁/T₂]ᶜ in the new system. Here n₂ = n₁ [M₁/M₂] [T₁/T₂]⁻².
3. The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). T: 1 second (s) is the same in both systems.
4. Put the numbers inn₂ = 1 [1 kg / 1 g] [1 s / 1 s]⁻²
5. Work out each bracket[M₁/M₂] = 1000; [T₁/T₂]⁻² = 1⁻² = 1
6. Multiplyn₂ = 1 × 1000 × 1 = 1,000
7. The answer1 N/m = 1,000 dyne/cm