1 \(30\;cm\;{s^{ - 1}}\)
2 \(28\;cm\;{s^{ - 1}}\)
3 \(24\;\,cm\;{s^{ - 1}}\)
4 \(32\;\,cm\;{s^{ - 1}}\)
Explanation:
Let the radius of bigger drop is \(R\) and that of smaller drop is \(r\) then
\(\frac{4}{3}\pi {R^3} = 8 \times \frac{4}{3} \times \pi {r^3}\)
\({\text{ or }}\quad R = 2r\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
Terminal velocity, \(v \propto r^{2}\)
\(\therefore \quad \frac{{{v^\prime }}}{v} = \frac{{{R^2}}}{{{r^2}}} = {\left( {\frac{{2r}}{r}} \right)^2} = 4\)
\( \Rightarrow \quad {v^\prime } = 4v = 4 \times 8 = 32\;cm\;{s^{ - 1}}\)