Final answer:
The viscosity of the liquid can be calculated using Stokes' law, which relates the viscosity to the terminal velocity of a small spherical object moving through the fluid. By substituting the given values into the formulas, the viscosity of the liquid is found to be 2.67 x 10^-4 Ns/m².
Step-by-step explanation:
To calculate the viscosity of the liquid, we can use Stokes' law, which relates the viscosity of a fluid to the terminal velocity of a small spherical object moving through the fluid.
The formula for Stokes' law is:
F = 6πηrv
Where F is the drag force, η is the viscosity, r is the radius of the object, and v is the velocity of the object.
Given the diameter of the bubble is 1 cm, the radius is 0.5 cm or 0.005 m. The distance it rises is 20 cm or 0.2 m, and the time is 4.5 seconds. The density of the bubble is 1.2 kg/m³.
We can calculate the velocity using the formula: v = d/t
Substituting the known values, we get: v = 0.2 m / 4.5 s = 0.044 m/s
With the radius and velocity, we can rearrange Stokes' law to solve for viscosity, η:
η = (F / (6πrv))
Since the drag force F is equal to the buoyancy force for a bubble, we can calculate it using: F = mg
Where m is the mass and g is the acceleration due to gravity. The mass can be calculated using: m = ρV
Where ρ is the density of the liquid and V is the volume of the bubble.
The volume of a sphere can be calculated using: V = (4/3)πr³
Substituting the known values and solving for the mass, we get: m = (1.2 kg/m³)(4/3)π(0.005 m)³ = 5.24 x 10^-6 kg
Finally, substituting the values for F, r, v, and m into the formula for viscosity, we get: η = (1.2 kg/m³)(9.8 m/s²)(0.2 m) / (6π(0.005 m)(0.044 m/s)) = 2.67 x 10^-4 Ns/m²