Question

If the time period $\left(T\right)$ of vibration of a liquid drop depends on surface tension $\left(S\right)$, radius $\left(r\right)$ of the drop and density $\left(p\right)$ of the liquid, then the expression of $T$ is

• A. $T=k\sqrt{pr^{3}/S}$
• B. $T=k\sqrt{pr^{1/2}r^{3}/S}$
• C. $T=k\sqrt{pr^{3}/S^{1/2}}$
• D. None of these

Answer 1

Answer: (A)

Let $T\propto S^{x}r^{y}p^{z}$
by substituting the dimension of $\left[T\right]=\left[T\right]$
$\left[S\right]=\left[MT^{-2}\right],\left[r\right]=\left[L\right],\left[\rho\right]=\left[ML^{-3}\right]$
and by comparing die power of both the sides
$x=-1/2, y=3/2, z=1/2$
so $T\propto\sqrt{\rho r^{3}/S}$
$\Rightarrow T=k\sqrt{\frac{\rho r^{3}}{S}}$