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Question

If the terminal speed of sphere A (density=19.5 kg/m3) is 0.2 m/s in a viscous liquid (density=1.5 kg/m3), find the terminal speed of a sphere B density=10.5 kg/m3) of the same size in the same liquid.

A
0.4 m/s
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B
0.133 m/s
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C
0.1 m/s
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D
0.2 m/s
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Solution

The correct option is C 0.1 m/s
Terminal speed of spherical body in a viscous liquid is given by
VT=2r2(ρσ)g9μ
where ρ = density of substance of a body.
σ = density of liquid.
μ=viscosity of the liquid.
From given data,
VT(B)VT(A)=ρBσρAσ
VT(B)=10.51.519.51.5×0.2
=918×0.2=0.1 m/s

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