Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ___

Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is

Q. Sixty four rain drops of radius 1 mm each falling down with a terminal velocity of 10 cm/s coalesce to form a bigger drop. The terminal velocity of bigger drop is ____ cm/s.

Correct Answer: 160

Explanation (Complete Step by Step Calculation)

For small spherical bodies moving through a viscous medium, terminal velocity is proportional to the square of the radius:

\[ v \propto r^2 \]

Let the radius of each small drop be \( r \) and terminal velocity be \( v = 10 \, \text{cm/s} \).

When 64 identical drops coalesce, volume is conserved:

\[ 64 \times \frac{4}{3}\pi r^3 = \frac{4}{3}\pi R^3 \]

\[ R^3 = 64 r^3 \]

\[ R = 4r \]

Now, terminal velocity of the bigger drop:

\[ \frac{v_2}{v_1} = \left(\frac{R}{r}\right)^2 \]

\[ \frac{v_2}{10} = (4)^2 \]

\[ v_2 = 10 \times 16 \]

\[ v_2 = 160 \, \text{cm/s} \]

Hence, the terminal velocity of the bigger drop is 160 cm/s.

Explanation (Complete Step by Step Calculation)

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