# Suppose A=B^nC^m, where A has dimensions, LT, B has dimensions L^2T^-1 and C has dimensions LT^2. Determine the dimensions of n and m values

Question

Suppose A=B^nC^m, where A has dimensions, LT, B has dimensions L^2T^-1 and C has dimensions LT^2. Determine the dimensions of n and m values.

in progress 0
1 year 2021-09-03T19:50:57+00:00 1 Answers 4 views 0

n = 1/5 and m = 3/5

Explanation:

The given quantity is :

$$A=B^nC^m$$

Where

The dimension of [A] = [LT]

The dimension of [B] = [L²T⁻¹]

The dimension of [C] = [LT²]

We need to find the dimensions of n and m values.

Using dimensional analysis,

$$[LT]=[L^2T^{-1}]^n[LT^2]^m\\\\\ [LT]=L^{2n}T^{-n}\times L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}$$

Comparing both sides,

2n+m=1 ….(1)

-n+2m=1 ,…..(2)

Solving (1) and (2), we get :

n = 1/5 and m = 3/5

Hence, this is the required solution.