Unit conversion

Convert 1 kg m/s into g cm/s using dimensional analysis

1 kg m/s = 100,000 g cm/s. Momentum is [M L T⁻¹], so only the powers of mass, length and time decide the factor.

Mass×10³1 kg = 1000 g

Length×10²1 m = 100 cm

Time×1s in both systems

1 kg m/s 100,000 g cm/s

Working

Step by step

The dimension of momentumMomentum has the dimensions [M L T⁻¹]. Only the powers of M, L and T matter for the conversion.
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] [L₁/L₂] [T₁/T₂]⁻¹.
The size of each base unitM: 1 kilogram (kg) is 1000 gram (g). L: 1 metre (m) is 100 centimetre (cm). T: 1 second (s) is the same in both systems.
Put the numbers inn₂ = 1 [1 kg / 1 g] [1 m / 1 cm] [1 s / 1 s]⁻¹
Work out each bracket[M₁/M₂] = 1000; [L₁/L₂] = 100; [T₁/T₂]⁻¹ = 1⁻¹ = 1
Multiplyn₂ = 1 × 1000 × 100 × 1 = 100,000
The answer1 kg m/s = 100,000 g cm/s

Questions

How do you convert kg m/s to g cm/s?

Momentum is [M L T⁻¹]. Multiply by the ratio of each base unit raised to its power in the dimension. That gives 1 kg m/s = 100,000 g cm/s.

What is 1 kg m/s in g cm/s?

1 kg m/s = 100,000 g cm/s.