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)

$\left[T^{-1}\right]={\left[L^1\right]}^a{\left[M^1{L}^{-3}\right]}^b{\left[\frac{ML{T}^{-2}}{L}\right]}^c$
$\Rightarrow T^{-1}=M^{b+c}\cdot L^{a-3b}\cdot T^{-2c}$
$c=\frac{1}{2},b=-\frac{1}{2},a-3b=0$
$a+\frac{3}{2}=0\Rightarrow a=-\frac{3}{2}$