First slide

Viscosity

Question

Two small spherical metal balls, having equal masses, are made from materials of densities ρ₁ and ρ₂(ρ₁ = 8ρ₂) and have radii of 1mm and 2mm, respectively. They are made to fall vertically (fromrest) in a viscous medium whose coefficient of viscosity equals η and whose density is 0.1ρ₂. The ratio of their terminal velocities would be

Moderate

A

79/72
B

19/36
C

39/72
D

79/36

Solution

As $\large V_T=\frac {2a^2}{9\eta}(\rho-\sigma)g$
$\large V_T=\frac {2\times (1)^2}{9\eta}(\rho_1-0.1\rho_2)g$
$\large V_{T_1}=\frac {2\times 1}{9\eta}(8\rho_2-0.1\rho_2)g....(i)$
$\large V_{T_2}=\frac {2\times (2)^2}{9\eta}(\rho_2-0.1\rho_2)g....(ii)$
$\large \therefore \frac {V_{T_1}}{V_{T_2}}=\frac {7.9}{4(0.9)}=\frac {79}{36}$

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