Final answer:
It is true that by measuring the terminal velocity of a spherical body in a liquid, one can determine the coefficient of viscosity of the liquid. This is achieved by using Stokes' law, which relates the drag force experienced by the spherical object to its velocity, the radius of the sphere, and the viscosity of the liquid.
Step-by-step explanation:
Yes, it is true that to determine the coefficient of viscosity of a given viscous liquid by measuring the terminal velocity of a given spherical body.
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
When a spherical object reaches terminal velocity in a viscous liquid, the net force on the object is zero because the gravitation force pulling the object downwards is balanced by the drag force exerted by the liquid and the buoyant force.
According to Stokes' law, the drag force Fs is given by the formula Fs = 6πνην, where ν is the object's velocity, η is the fluid's viscosity, and R is the radius of the spherical object.
In the given scenario, a steel ball bearing with a density of 7.8 × 10³ kg/m³ and a diameter of 3.0 mm is dropped in a container of motor oil and takes 12 s to fall a distance of 0.60 m. To calculate the viscosity of the oil, we must first determine the terminal speed of the ball bearing which can be found by dividing the distance by the time taken to fall that distance.
Once we have the terminal speed, we can plug the known values into Stokes' law to determine the viscosity of the motor oil.