The frequency (ν) of an oscillating liquid drop may depend upon...

Here, we have $ν = {r}^{a}{ρ}^{b}{s}^{c}$

Equating the dimensions of each quantity on both sides

\left[{T}^{- 1}\right] = {\left[{L}^{1}\right]}^{a}{\left[{M}^{1}{L}^{- 3}\right]}^{b}{\left[\dfrac{ML{T}^{- 2}}{L}\right]}^{c} ⇒ {T}^{- 1} = {M}^{b + c}{L}^{a - 3b}{T}^{- 2c}$</p><p>Comparing the dimensions, we get</p><p>$c = \dfrac{1}{2}, b = - \dfrac{1}{2}, a - 3b = 0$</p><p>$⇒ a + \dfrac{3}{2} = 0 ⇒ a = - \dfrac{3}{2}$</p><p>Thus, the value of$a$,$b and c$are \left(- \dfrac{3}{2}, - \dfrac{1}{2}, \dfrac{1}{2}\right)$.