N identical spherical drops, each of radius r, fall through the same viscous medium with terminal speed v. They coalesce completely into one spherical drop of the same material. Assuming Stokes' law remains valid, what is the terminal speed of the new drop?
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Question

N identical spherical drops, each of radius r, fall through the same viscous medium with terminal speed v. They coalesce completely into one spherical drop of the same material. Assuming Stokes' law remains valid, what is the terminal speed of the new drop?

Options

G1 Physics · Accepted Answer

By conservation of volume, R³ = Nr³. Therefore, R = r∛N. For the same drop material and surrounding medium, vₜ ∝ r². Hence, v(new)/v = R²/r² = (∛N)². Therefore, v(new) = v(∛N)². Correct option: B.