Question

Eight drops of equal size are falling through air- with steady velocity of $10cm/s$. If the drop; coalesce, what could be its terminal velocity

• A. 40 cm/s
• B. 20 cm/s
• C. 25 cm/s
• D. 50 cm/s

Answer 1

Answer: (A)

Let $R$ be radius of coalesced drop, and $r$ the radius of $8$ small drops. Also,
Mass of coalesced drop $=8\times$ mass of small drop
$\Rightarrow \frac{4}{3}\pi R^3\times \rho$
$=8\times \frac{4}{3}\pi r^3\times \rho$
$\Rightarrow R=2r$
Also terminal velocity
$v_T=\frac{2}{9}\frac{(\rho -\sigma )r^{2}g}{\eta }$ ...(i)
and of coalesced drop is
$v_T^{\prime }=\frac{2}{9}\frac{(\rho -\sigma )R^{2}g}{\eta }$ ...(ii)
From Eqs. (i) and (ii), we get
$\frac{v_T^{\prime }}{v_T}={\left(\frac{R}{r}\right)}^2=(2{)}^2=4$
$\therefore v_T^{\prime }=4\times 10=40cm/s$