Explanation:
The expression is :
[tex]A=B^nC^m[/tex]
A =[LT], B=[L²T⁻¹], C=[LT²]
Using dimensional of A, B and C in above formula. So,
[tex]A=B^nC^m\\\\\ [LT]=[L^2T^{-1}]^n[LT^2}]^m\\\\\ [LT]=L^{2n}T^{-n}L^mT^{2m}\\\\\ [LT]=L^{2n+m}T^{2m-n}[/tex]
Comparing the powers both sides,
2n+m=1 ...(1)
2m-n=1 ...(2)
Now, solving equation (1) and (2) we get :
[tex]n=\dfrac{1}{5}\\\\m=\dfrac{3}{5}[/tex]
Hence, the correct option is (E).
The values of the exponents n and m are [tex]\frac{1}{5}[/tex] and [tex]\frac{3}{5}[/tex] respectively.
The given parameters;
[tex]A = B^nC^m[/tex]
[tex]A = LT\\\\B = L^2T^{-1}\\\\C = LT^2[/tex]
The values of the given exponents "n" and "m" are calculated as follows;
[tex]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)[/tex]
from equation(2);
[tex]n = 2m - 1[/tex]
substitute the value of n into equation (1);
[tex]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}[/tex]
Thus, the values of the exponents n and m are [tex]\frac{1}{5}[/tex] and [tex]\frac{3}{5}[/tex] respectively.
Learn more here:https://brainly.com/question/24704345
