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Q.

Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2ρ1=8ρ2 and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.12ρ2. The ratio of their terminal velocities would be

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a

1936

b

3972

c

7972

d

7936

answer is D.

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Detailed Solution

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VT=2r2(σρ)g9η

V1V2=r1r22σ1ρσ2ρ

=1228ρ20.1ρ2ρ20.1ρ=7936

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Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2ρ1=8ρ2 and have radii of 1mm and 2mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.12ρ2. The ratio of their terminal velocities would be