Question

Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is ______.

पर्याय

• 10 cm/s

• 40 cm/s

• 16 cm/s

• 5 cm/s

Answer 1

Eight equal drops of water are falling through air with a steady speed of 10 cm/s. If the drops coalesce, the new velocity is 40 cm/s.

Explanation:

When 8 small drops (radius r) combine into one big drop (radius R), the volume remains constant:

`4/3 pi R^3 = 8 xx (4/3 pi r^3)`

R³ = 8r³

R = 2r

The steady speed (terminal velocity v) is proportional to the square of the radius:

v ∝ r²

or

`v_1/v_2 = (r_1/r_2)^2`

`v_"old"/v_"new" = (r/R)^2`

`10/v_"new" = (r/(2r))^2`

= `(1/2)^2`

`10/v_"new" = 1/4`

v_new = 10 × 4

= 40 cm/s