The acceleration of a body when falling through viscous medium is
Correct answer: D. a = 6πηrV/m - g
- A. 0
- B. g
- C. 6πηrV-mg
- D. a = 6πηrV/m - g
Explanation
The correct answer is a = 6πηrV/m - g. When a body falls through a viscous medium, it experiences a drag force in addition to gravitational force. The viscous drag force is given by 6πηrV, where η is the viscosity of the medium, r is the radius of the body, and V is the velocity. The net force acting on the body is the difference between gravitational force (mg) and the viscous drag force. The acceleration is then the net force divided by the mass of the body, (6πηrV - mg)/m, which simplifies to the correct option. Other options either neglect the viscous force or do not correctly apply Newton's second law to solve for acceleration.
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About Fluid Dynamics
Fluid flow is described through speed, pressure and density, including steady flow and the equation of continuity for conserving mass. Bernoulli's equation relates pressure, speed and height, while fluid drag and terminal velocity explain why a falling object eventually moves at constant speed when drag balances its weight.
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