Question

Frequency is the function of density ( $\rho$ ), length $(a)$ and surface tension $(T)$ The value is:

• A. $\frac{k{\rho }^{1/2}{a}^{3/2}}{\sqrt{T}}$
• B. $\frac{k{\rho }^{3/2}{a}^{3/2}}{\sqrt{T}}$
• C. $\frac{k{\rho }^{1/2}{a}^{3/2}}{T^{3/4}}$
• D. None of these

Answer 1

Answer: (D)

Let $n=k{\rho }^a{a}^b{T}^c$ where $[p]=\left[M{L}^{-3}\right],[a]=[L]$ and
$[T]=\left[M{T}^{-2}\right]$
Comparing dimensions both sides, we get-
$a=-1/2,b=-3/2$ and $c=1/2$
$\therefore \eta =k{\rho }^{-1/2}{a}^{-3/2}{T}^{-1/2}$
$=\frac{k\sqrt{T}}{{\rho }^{1/2}{a}^{3/2}}$