Question

A spherical rain drop of mass \(m\) falls vertically through air with a terminal velocity of \(0.2\ \mathrm{ms^{-1}}\). If \(27\) such identical rain drops combine to form a bigger spherical drop, then the terminal velocity of the bigger drop if it falls vertically through air is

• A. \(0.9\ \mathrm{ms^{-1}}\)
• B. \(3.6\ \mathrm{ms^{-1}}\)
• C. \(5.4\ \mathrm{ms^{-1}}\)
• D. \(1.8\ \mathrm{ms^{-1}}\)

Hint:

According to Stokes' law, \[ \boxed{v_t\propto r^2.} \] If \(n\) identical drops combine, \[ \boxed{R=n^{1/3}r.} \] Hence, \[ \boxed{v_t\propto n^{2/3}.} \]

Answer 1

The Correct Option is D