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The terminal velocity of a copper ball of radius 2 mm falling through a tank of honey is 30 mm/s. What will be the drag force exerted by the oil on the copper ball if the viscosity of the oil is 1 N-s/m2.
1. 1.13 × 10-4 N
2. 1.13 × 10-6 N
3. 36 × 10-4 N
4. 36 × 10-6 N

1 Answer

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Correct Answer - Option 1 : 1.13 × 10-4 N

CONCEPT

  • Viscosity: The state of being sticky, thick, and semi-fluid inconsistency, due to internal friction of fluids is called viscosity.
  • Stokes Law: This law tells about the viscous drag force when a sphere goes with a terminal velocity v inside a liquid.

By this law viscous drag force is given by

F = 6πηrv

where r is the radius of the sphere, v is the velocity, and η is the viscosity of the fluid.

CALCULATION:

Given that r = 2 mm = 2 × 10-3 m; v = 30 mm/s = 30 × 10-3 m/s; η = 1 N-s/m2

viscous drag force F = 6πηrv

F = 6π × 1 × 2 × 10-3 × 30 × 10-3 

F = 36π × 10-6 N

F = 1.13 × 10-4 N

So the correct answer is option 1.

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