A solid sphere has terminal speed 90 cm/s in a viscous liquid. It is broken into 27 identical spherical pieces made of the same material. Assuming Stokes' law remains valid for each piece, if the terminal speed of each smaller sphere is N cm/s, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A solid sphere has terminal speed 90 cm/s in a viscous liquid. It is broken into 27 identical spherical pieces made of the same material. Assuming Stokes' law remains valid for each piece, if the terminal speed of each smaller sphere is N cm/s, find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

When one sphere is broken into 27 identical spheres, R³ = 27r³. Therefore, r = R/3. Terminal speed varies as the square of the radius: vₜ ∝ r². Hence, v(small) = 90×(1/3)² = 90/9 = 10 cm/s. Therefore, N = 10.