Question

A liquid drop of density $\rho$, radius $r$, and surface tension $\sigma$ oscillates with time period $T$. Which of the following expressions for $T^{2}$ is correct?

• A. $\frac{\rho r^{3}}{\sigma}$
• B. $\frac{\rho \sigma}{r^{3}}$
• C. $\frac{r^{3} \sigma}{\rho}$
• D. None of these

Answer 1

Answer: (A)

Let $T^{2}=\rho^{a} r^{b} \sigma^{c}$
$T^{2}=\left(M L^{-3}\right)^{a}(L)^{b}\left(M T^{-2}\right)^{c}=M^{a+c} L^{-3 a+b} T^{-2 c}$
$a+c=0,-3 a+b=0$, and $-2 c=2$
Hence, $a=1, b=3$, and $c=-1$
$T^{2}=\rho r^{3} \sigma^{-1}=\frac{\rho r^{3}}{\sigma}$