GATE 2025 MT – Question 54
Spherical galena particles have the same settling velocity in water as spherical quartz particles of diameter 25 μm. The galena diameter is ______ μm (rounded to one decimal place). Assume Stokes settling. Given densities: galena 7400, quartz 2600, and water 1000 kg m$^{-3}$.
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Correct answer: 12.5 to 12.5
Explanation
Stokes’ terminal velocity is $v=(\rho_p-\rho_f)gd^2/(18\mu)$. For equal velocities in the same liquid, $(7400-1000)d_g^2=(2600-1000)25^2$.
Thus $d_g=25\sqrt{1600/6400}=\boxed{12.5\ \mu\mathrm m}$.