The period of a body under Simple Hormonic Motion is represented by T = P^a D^b S^c. Where P is pressure, D is density, and S is surface tension. Then the value of a, b, c...???
Please explain me clearly....
Please explain me clearly....
1 Answer
Apr 9, 2018
Explanation:
Your claim is that:
By dimensional analysis:
Surface tension is accounted for here as force per unit length. If your understanding is different, adjust the calculation.
So:
Working mechanically through the exponentiation, this gives 3 equations in 3 unknowns:
-
kg:
\qquad a + b + c = 0 -
m:
\qquad -a - 3b = 0 -
s:
\qquad -2a - 2 c = 1
It solves as:
Dimensionally at least, the following should hold: