The velocity of small spherical ball of mass ' m ' and density ' d₁ ', when dropped in a container filled with glycerine becomes constant after some time. The viscous force acting on the ball if density of glycerine is ' d ₂ ' is

Step-by-step solution

At terminal velocity, the net force on the spherical ball must be zero, with gravitational, buoyant, and viscous forces in equilibrium. The gravitational force is W = mg , while the buoyant force equals the weight of displaced fluid. The volume of the sphere is V = m d₁ , so F_B = V d₂ g = mg d₂ d₁ . Balancing the forces gives F_V + F_B = W , which becomes F_V + mg d₂ d₁ = mg . Solving for viscous force yields F_V = mg - mg d₂ d₁ = mg (1 - d₂ d₁ ) . The expression mg (1 - d₂ d₁ ) corresponds to option A.