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.

Answer 1

Answer:

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.