A solid sphere of volume V and density is falling through a liquid of density . If the sphere has attained terminal velocity, what is the magnitude of the viscous drag force acting on it in terms of the given parameters? (where g is the acceleration due to gravity)

Step-by-step solution

When the sphere attains terminal velocity, it moves with a constant velocity, meaning the net force acting on it is zero. The forces acting on the sphere are: 1. Downward weight, W = V g 2. Upward buoyant force, F_B = V g 3. Upward viscous drag force, F_v For equilibrium at terminal velocity: W = F_B + F_v Rearranging for the viscous drag force: F_v = W - F_B F_v = V g - V g = V( - )g Answer: V( - )g