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)

$\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$

Answer 2

The correct answer is (B) : $\left(-\frac{3}{2},-\frac{1}{2}, \frac{1}{2}\right)$
[T−1]=[L1]a[M1L−3]b[LMLT−2​]c
⇒T−1=Mb+c⋅La−3b⋅T−2c
c=21​,b=−21​,a−3b=0
a+23​=0⇒a=−23​