A liquid drop of density \(\rho\), radius r, and surface tension \(\sigma\) oscillates with time period T. Which of the following expressions for T2 is correct ?

\(\frac{\rho r^3}{\sigma}\) \(\frac{\rho \sigma}{r^3}\) \(\frac{\sigma r^3}{\rho}\) None of these.

\(\frac{\rho r^3}{\sigma}\)

Let : T2 = \(\rho^a r^b \sigma^c\) T2 = [ML-3]a [L]b [MT-2]c On solving : a = 1, b = 3 and c = -1 T2 = \(\rho^1 r^3 \sigma^{-1}\) T2 = \(\frac{\rho r^3}{\sigma}\)