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Question

The terminal speed of a sphere of gold (density = 19.5 g/cm3) is 0.2 m/s in a viscous liquid (density = 1.5 g/cm3). Find the terminal speed of a sphere of silver (density =10.5 g/cm3) of the same size in the same liquid (in m/s)

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Solution

Given, ρg=19.5 g/cm3 (density of gold)
ρl=1.5 g/cm3 (density of liquid)
ρs=10.5 g/cm3 (density of silver)
Terminal speed of sphere of sphere of gold, vg=0.2 m/s
Let the terminal speed of sphere of silver =vs

Terminal velocity of any body is given by (v)=2(ρbρl)r2g9μ
Both sphere of gold & silver are of same size.
So, Terminal velocity (ρbρl)
where ρb= density of spheres
ρl = density of liquid
vgvs=(ρgρl)(ρsρl)
0.2vs=(19.51.5)(10.51.5)
vs=0.1 m/s

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