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

n = 1/5 and m = 3/5

Step-by-step 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)* 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.