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The frequency $(v)$ of an oscillating liquid drop may depend upon radius $(r)$ of the drop, density $(\rho)$ of liquid and the surface tension $(s)$ of the liquid as : $v=r^{ a } \rho^{ b } s ^{ c }$. The values of $a , b$ and $c$ respectively are
$\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
$\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)$
$\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)$
Solution
${\left[ T ^{-1}\right]=\left[ L ^1\right]^{ a }\left[ M ^{ 1 } L ^{-3}\right]^{ b }\left[\frac{ MLT ^{-2}}{ L }\right]^{ c }}$
$\Rightarrow T ^{-1}= M ^{ b + c } \cdot L ^{ a -3 b } \cdot T ^{-2 c}$
$c =\frac{1}{2}, b =-\frac{1}{2}, \quad a -3 b =0$
$a +\frac{3}{2}=0 \Rightarrow a =-\frac{3}{2}$
