Answer:
n = 1/5 and m = 3/5
Explanation:
The given quantity is :
[tex]A=B^nC^m[/tex]
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,
[tex][LT]=[L^2T^{-1}]^n[LT^2]^m\\\\\ [LT]=L^{2n}T^{-n}\times L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}[/tex]
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.