Two small spherical metal balls, having equal masses, are made from materials of densities $ρ_{1}$ and $ρ_{2} (ρ_{1} = 8 ρ_{2})$ 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 $0.12 ρ_{2} .$ The ratio of their terminal velocities would be

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$\frac{19}{36}$

$\frac{39}{72}$

$\frac{79}{72}$

$\frac{79}{36}$

answer is D.

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Detailed Solution

$V_{T} = \frac{2 r^{2} (σ - ρ) g}{9 η}$

$\frac{V_{1}}{V_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} \frac{(σ_{1} - ρ)}{(σ_{2} - ρ)}$

$= {(\frac{1}{2})}^{2} \frac{(8 ρ_{2} - 0.1 ρ_{2})}{(ρ_{2} - 0.1 ρ)} = \frac{79}{36}$

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