A hypothetical system of units is created where the fundamental unit of mass is kg , the fundamental unit of length is m , and the fundamental unit of time is s . The magnitude of a 1 N force when expressed in this hypothetical system is :

Step-by-step solution

The dimensional formula of force is [MLT⁻²] . Let the SI system be system 1 and the hypothetical system be system 2. Using the principle of conversion of units, n₁[u₁] = n₂[u₂] : n₁ [M₁ L₁ T₁⁻²] = n₂ [M₂ L₂ T₂⁻²] Given that n₁ = 1 , M₁ = 1 kg , L₁ = 1 m , T₁ = 1 s and M₂ = kg , L₂ = m , T₂ = s . 1 [1 kg ] [1 m ] [1 s ]⁻² = n₂ [ kg ] [ m ] [ s ]⁻² n₂ = 1 ( 1 ) ( 1 ) ( 1 )⁻² n₂ = ^2 Answer: ^2