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

Answer 1

Answer: (A)

Let $T\propto S^x{r}^y{p}^z$

by substituting the dimension of $\left[T\right]=\left[T\right]$

$\left[S\right]=\left[M{T}^{-2}\right],\left[r\right]=\left[L\right],\left[\rho \right]=\left[M{L}^{-3}\right]$

and by comparing die power of both the sides

$x=-1/2,y=3/2,z=1/2$

so $T\propto \sqrt{\rho r^3/S}$
$\Rightarrow T=k\sqrt{\frac{\rho r^3}{S}}$