The question is: If the radii of two droplets are in the ratio 2:3, what will be the ratio of their Terminal velocities?
Correct answer: C. 4:9
- A. 2:3
- B. 4:6
- C. 4:9
- D. 2:6
Explanation
The terminal velocity of a spherical object falling through a viscous fluid is directly proportional to the square of its radius. This is given by the following equation:v = (2/9) * (ρ - ρ') * g * r^2 / ηwhere:v is the terminal velocityρ is the density of the objectρ' is the density of the fluidg is the acceleration due to gravityr is the radius of the objectη is the viscosity of the fluidSince the densities, acceleration due to gravity, and viscosity are constant for both droplets, the ratio of their terminal velocities is directly proportional to the square of the ratio of their radii.Therefore, if the radii of the two droplets are in the ratio 2:3, their terminal velocities will be in the ratio (2^2) : (3^2) = 4:9.
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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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