Two small spherical metal balls, having equal masses, are made from materials of densities and 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 and who

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Solution

Q.
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 [2019]

1 $\frac{79}{72}$

2 $\frac{19}{36}$

3 $\frac{39}{72}$

4 $\frac{79}{36}$

Ans.
(4)

Terminal velocity, $v = \frac{2 r^{2} (ρ - σ) g}{9 η}$

Ratio of terminal velocity of spherical metal balls,

$\frac{v_{1}}{v_{2}} = \frac{\frac{2}{9} {(1)}^{2} (8 ρ_{2} - 0.1 ρ_{2})}{\frac{2}{9} {(2)}^{2} (ρ_{2} - 0.1 ρ_{2})} \Rightarrow \frac{v_{1}}{v_{2}} = \frac{7.9 ρ_{2}}{4 (0.9 ρ_{2})} = \frac{79}{36}$

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