Question

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

• A. $\left(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2}\right)$
• B. $\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
• C. $\left(\frac{3}{2}, \frac{1}{2},-\frac{1}{2}\right)$
• D. $\left(\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$

Answer 1

Answer: (B)

$ {\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}, a -3 b =0$
$a +\frac{3}{2}=0 \Rightarrow a =-\frac{3}{2}$