Question

'$n$' small water drops of same size (radius $r$) fall through air with constant velocity V. They coalesce to form a big drop of radius R. The terminal velocity of the big drop is

• A. $\frac{\text{VR}^2}{\text{r}^2}$
• B. $\frac{\text{Vr}^2}{\text{R}^2}$
• C. $\frac{VR}{r}$
• D. $\frac{\text{Vr}}{\text{R}}$

Hint:

Since volume is conserved, $R = n^{1/3}r$. Terminal velocity becomes $n^{2/3}V$.

Answer 1

The Correct Option is A

Step 1: Concept
Terminal velocity $v_t$ is proportional to the square of the radius ($v_t \propto r^2$).

Step 2: Meaning
For small drops, $V = k r^2$. For the big drop, $V_{big} = k R^2$.

Step 3: Analysis
Taking the ratio: $V_{big} / V = R^2 / r^2$.

Step 4: Conclusion
$V_{big} = \frac{VR^2}{r^2}$. Final Answer: (A)