First slide

Viscosity

Question

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 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 $0.1 ρ_{2}$ . The ratio of their terminal velocities would be,

Moderate

A

$\frac{79}{36}$
B

$\frac{79}{73}$
C

$\frac{19}{36}$
D

$\frac{39}{72}$

Solution

$As V_{T} = \frac{2 a^{2}}{9 η} (ρ - σ) g V_{T_{1}} = \frac{2 \times (1)^{2}}{9 η} (ρ_{1} - 0.1 ρ_{2}) g V_{T_{1}} = \frac{2 \times 1}{9 η} (8 ρ_{2} - 0.1 ρ_{2}) g . . . . (i) V_{T_{2}} = \frac{2 \times (2)^{2}}{9 η} (ρ_{2} - 0.1 ρ_{2}) g . . . (ii) ∴ \frac{V_{T_{1}}}{V_{T_{2}}} = \frac{7.9}{4 (0.9)} = \frac{79}{36}$

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