Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2 (ρ1 = 8ρ2) and have radii of 1 mm and 2 mm, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ2 . The ratio of their terminal velocities would be,
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a
7936
b
7973
c
1936
d
3972
answer is A.
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Detailed Solution
As VT=2a29η(ρ-σ)g VT1=2×(1)29ηρ1-0.1ρ2g VT1=2×19η8ρ2-0.1ρ2g ....(i) VT2=2×(2)29ηρ2-0.1ρ2g ...(ii) ∴VT1 VT2=7.94(0.9)=7936
Two small spherical metal balls, having equal masses, are made from materials of densities ρ1 and ρ2 (ρ1 = 8ρ2) and have radii of 1 mm and 2 mm, respectively, they are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ2 . The ratio of their terminal velocities would be,