Answer to Question #158496 in Classical Mechanics for gülay

Question

In A = B" C" expression, A has a dimension of [LT], and B has a dimension of [L*T| IfC has a dimension of [L'T), find the value of m+n.

Answer 1

$$[A]=[B]^n[C]^m\\ [LT]=[L^2T^{-1}]^n[LT^2]^m\\ 1=2n+m\\1=-n+2m$$

$$1=-n+2(1-2n)\\n=\frac{1}{5}\\m=1-2\frac{1}{5}=\frac{3}{5}\\m+n=\frac{4}{5}$$