A small solid sphere of mass M and density d₁ is released from rest at the bottom of a deep tank filled with a liquid of density d₂ (where d₂ > d₁ ). It rises and eventually attains a constant upward velocity. The magnitude of the viscous force acting on the sphere when it is moving with this constant velocity is

Step-by-step solution

When the sphere attains a constant upward velocity, it is in a state of dynamic equilibrium, meaning the net force acting on it is zero. The forces acting on the sphere are: 1. Upward buoyant force, F_b 2. Downward gravitational force, Mg 3. Downward viscous force, F_v (since viscous drag always opposes the direction of motion). Equating the upward and downward forces: F_b = Mg + F_v F_v = F_b - Mg The buoyant force is given by the weight of the displaced liquid: F_b = V d₂ g Since the volume of the sphere is V = M