Question

Two rain drops of same radius '\(r\)' falling with same terminal velocity '\(V\)' merge and form bigger drop of radius '\(R\)'. The terminal velocity of big drop is

• A. \(\frac{VR^2}{r^2}\)
• B. \(\frac{2VR}{r}\)
• C. \(\frac{VR}{r}\)
• D. \(Vr^2/R^2\)

Hint:

Terminal velocity varies as the square of the radius, and volume is conserved on merging.

Answer 1

The Correct Option is A

Step 1: Compare big and small drop
$\frac{V_{big}}{V_{small}}=\left(\frac{R}{r}\right)^2$ because the other quantities are the same. Hence $V_{big}=V\frac{R^2}{r^2}$. Option (A).
Numerically $\frac{R}{r}=2^{1/3}$, so the speed increases by about $1.59$ times.

Final Answer:
Option (A). \[ \boxed{\text{(A)}} \]