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