Question

Frequency is the function of density(rho), length(l) and surface tension (T). Then its value is ??
(Answer is k p^1/2 L^-1/2 T^-3/2)

Answer 1

frequency(f) is the function of density($\rho$) , length (l), and surface tension (T)

we can write it , $f\propto\rho^xl^yT^z$

dimension of f = [ T^-1 ]

dimension of $\rho$ = [ML^-3]

dimension of L = [L]

dimension of T = [MT^-2]

so, $[T^{-1}]\propto[ML^{-3}]^x[L]^y[MT^{-2}]^z$

or, $[M^0L^0T^{-1}]\propto [M]^{x+z}[L]^{-3x+y}[T]^{-2z}$

comparing both sides,

x + z = 0, ......(1)

-3x + y = 0......(2)

-2z = -1 => z = 1/2 .....(3)

from equations (1), (2) and (3),

x = -1/2 , y = 3x = -3/2 and z = 1/2

hence, $f\propto \rho^{-1/2}l^{- 3/2}T^{1/2}$

[your given is wrong btw , you can check your answer by using dimension formula of all terms ]

Answer 2

Answer;

Below is the Full answer with method

Hope you understand answer

Thanks ..