Physics: Suppose A=BnCm, where A has dimensions LT, B has dimensions L2T-1, and C has dimensions LT2. Then the exponents n and m have the values?A. 2; 3B. 2/3; 1/3C. 4/5; -1/5D. 1/2; 1/2E. 1/5; 3/5

Suppose A=BnCm, where A has dimensions LT, B has

Ответ:

jacobballew2019

01.02.2022

Physics

The values of the exponents n and m are $\frac{1}{5}$ and $\frac{3}{5}$ respectively.

The given parameters;

A = B^nC^m

$A = LT\\\\B = L^2T^{-1}\\\\C = LT^2$

The values of the given exponents "n" and "m" are calculated as follows;

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

from equation(2);

n = 2m - 1

substitute the value of n into equation (1);

$1 = 2(2m-1) + m\\\\1 = 4m - 2 + m\\\\1 = 5m - 2\\\\3 = 5m\\\\m = \frac{3}{5} \\\\n = 2m - 1\\\\n = 2(\frac{3}{5} ) - 1\\\\n = \frac{6}{5} - 1 \\\\n = \frac{1}{5}$