First slide

Viscosity

Question

Two equal drops are falling through air with a steady velocity of 5 cm/sec. If the drops coalesce, the new terminal velocity will be

Easy

A

5x 2cm/sec
B

$5 x \sqrt{2 cm / \sec}$
C

$5 \times (4)^{1 / 3} cm / \sec$
D

$5 / \sqrt{2} cm / \sec$

Solution

$v_{T} \propto r^{2} . Hence 5 \propto r^{2} and v \propto R^{2} or v \propto {\{(2)^{1 / 3} r\}}^{2} \propto 4^{1 / 3} r^{2} ∴ \frac{v}{5} = (4)^{1 / 3} or V = 5 \times (4)^{1 / 3} cm / \sec$

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