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NEET 2019 · Terminal Velocity

Terminal Velocity question from NEET 2019

Q50NEET 2019Medium

Terminal Velocity

Two small spherical metal balls, having equal masses, are made from materials of densities ρ1\rho_1 and ρ2\rho_2 (ρ1=8ρ2\rho_1 = 8\rho_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\eta and whose density is 0.1ρ20.1\rho_2. The ratio of their terminal velocities would be,

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Answer: (a)

  1. vt=2r2(ρ−σ)g9η⇒v∝r2(ρ−σ)v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta} \Rightarrow v \propto r^2(\rho - \sigma), with σ=0.1ρ2\sigma = 0.1\rho_2.
  2. v1v2=12(8ρ2−0.1ρ2)22(ρ2−0.1ρ2)=7.94×0.9\dfrac{v_1}{v_2} = \dfrac{1^2(8\rho_2 - 0.1\rho_2)}{2^2(\rho_2 - 0.1\rho_2)} = \dfrac{7.9}{4 \times 0.9}
  3. =7.93.6=7936= \dfrac{7.9}{3.6} = \dfrac{79}{36}
  4. So the answer is (a) 7936\frac{79}{36}.
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