Final answer:
The viscous force experienced by an object moving through a fluid is directly proportional to the object's velocity v, as given by option c) f ∝ v. The relationship does not depend directly on the object's mass m.
Step-by-step explanation:
The relationship between the mass m, speed v, and viscous force f of an object moving through a fluid is not as straightforward as a simple multiplication or division. According to the principles of fluid dynamics, the viscous force experienced by an object moving in a fluid is typically dependent on the object's speed and other factors such as the shape and size of the object, the fluid's viscosity, and in certain cases, the square of the velocity. However, if we are dealing with laminar flow and the object's motion resembling that described by Stoke's law, the viscous drag Fs is proportional to the product of the fluid's viscosity n, the characteristic size of the object L, and its velocity v, as given by Fs = 6πRnv for a small sphere.
From the given options, c) f ∝ v is the most accurate, as it signifies that the viscous force f is directly proportional to the speed v, which aligns with the experimental observations described for laminar flow conditions. There is no direct proportionality indicated between the mass m and the viscous force f, making option d) incorrect. Options a) and b) are not supported by the principles of fluid mechanics as described.