Final answer:
Correct option: c) Quadrupled
The terminal velocity of a sphere in a viscous fluid quadruples when its radius is doubled, according to the derived formula for terminal velocity using Stokes' Law.
Step-by-step explanation:
To determine how the terminal velocity changes when a spherical object's radius in a viscous fluid is doubled, we need to understand the forces at play. In particular, at terminal velocity, a spherical object's gravitational force is balanced by the drag force and the buoyant force.
Stokes' Law is used for small, spherical objects moving through a fluid at low Reynolds numbers, where the drag force Fs is given by 6πηrv, with r being the radius, η the viscosity of the fluid, and v the velocity of the object.
The equation for terminal velocity V is derived as follows: V = (2(Ps - P1)R²) / (9η), where Ps is the density of the sphere, P1 is the density of the fluid, and R is the radius of the sphere.
Doubling the radius therefore results in a change in terminal velocity to 4V, meaning the velocity becomes quadrupled.
Regarding the other aspects of terminal velocity, changes in size, shape, or velocity of the falling object or the viscosity of the liquid will affect the terminal speed differently, depending on the situation.