Units And Dimensions Question 2
Question 2 - 24 January - Shift 2
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
(1) $(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2})$
(2) $(\frac{3}{2},-\frac{1}{2}, \frac{1}{2})$
(3) $(\frac{3}{2}, \frac{1}{2},-\frac{1}{2})$
(4) $(-\frac{3}{2}, \frac{1}{2}, \frac{1}{2})$
Show Answer
Answer: (1)
Solution:
Formula: Dimensional equation
$ \begin{aligned} & {[T^{-1}]=[L^{1}]^{a}[M^{1} L^{-3}]^{b}[\frac{MLT^{-2}}{L}]^{c}} \\ & \Rightarrow T^{-1}=M^{b+c} \cdot L^{a-3 b} \cdot T^{-2 c} \end{aligned} $
$c=\frac{1}{2}, b=-\frac{1}{2}, \quad a-3 b=0$
$a+\frac{3}{2}=0 \Rightarrow a=-\frac{3}{2}$
