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A spherical ball of density ρ and radius 0 . 003 m is dropped into a tube containing a viscous fluid, filled up to the 0 cm mark as shown in the figure. Viscosity of the fluid = 1 . 260 N m - 2 s - 1 and its density ρ L = ρ / 2 = 1260 kg m - 3 . Assume the ball reaches a terminal speed by the 10 cm mark. Find the time taken by the ball to traverse the distance between the 10 cm and 20 cm mark. [ g = acceleration due

Options

  1. A2 s
  2. B3   s
  3. C5 s
  4. D1.5   s

Correct answer

C. 5 s

Step-by-step solution

Terminal Velocity: V T = 2 9 × r 2 ρ - ρ L g η ⇒ V T = 2 9 × 3 × 1 0 - 3 2 × 1 2 6 0 × 10 1 . 2 6 0 V T = 2 × 10 - 2 m s - 1 ⇒ V T = 2 cm s - 1 t = 10 cm V T ⇒ t = 5 s

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