How is one system of units converted to another with the help of dimen

1.	How is one system of units converted to another with the help of dimensions?
Answer» Let a physical quantity be given by A = n₁u₁ = n₂u₂ where n₁ is numerical value with u₁ as unit in one system and similarly n₂is numerical value with u₂ as unit in another system. If dimensional formula of A is [M^aL^bT^c ] then, n₁ [M₁^aL₁^bT₁^c ] = n₂[M₂^aL₂^bT₂^c ] i.e., \(n_2 = n_1\frac{[M_1^aL_1^bT_1^c]}{[M_1^aL_1^bT_1^c]}\) = \(n_1[\frac{M_1}{M_2}]^a\)\([\frac{L_1}{L_2}]^b\)\([\frac{T_1}{T_2}]^c\)

How is one system of units converted to another with the help of dimensions?

Answer»

Let a physical quantity be given by

A = n₁u₁ = n₂u₂

where n₁ is numerical value with u₁ as unit in one system and similarly n₂is numerical value with u₂ as unit in another system.

If dimensional formula of A is [M^aL^bT^c ]

then, n₁ [M₁^aL₁^bT₁^c ] = n₂[M₂^aL₂^bT₂^c ]

i.e., \(n_2 = n_1\frac{[M_1^aL_1^bT_1^c]}{[M_1^aL_1^bT_1^c]}\)

= \(n_1[\frac{M_1}{M_2}]^a\)\([\frac{L_1}{L_2}]^b\)\([\frac{T_1}{T_2}]^c\)