If the terminal speed of a sphere of gold (density = 19.5 kg m⁻³) is 0.2 m s⁻¹ in a viscous liquid (density = 1.5 kg m⁻³), find the terminal speed of a sphere of silver (density = 10.5 kg m⁻³) of the same size in the same liquid.
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Question

If the terminal speed of a sphere of gold (density = 19.5 kg m⁻³) is 0.2 m s⁻¹ in a viscous liquid (density = 1.5 kg m⁻³), find the terminal speed of a sphere of silver (density = 10.5 kg m⁻³) of the same size in the same liquid.

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G1 Physics · Accepted Answer

Step 1: Use viscous-force relations: shear F = ηA(dv/dy), Stokes force 6πηrv, or Reynolds number Re = ρvD/η as appropriate. Step 2: At terminal speed set net weight/buoyancy equal to viscous drag and use the given geometry. Applying these relations to the given data gives C: 0.1 m s⁻¹. Final answer: C.