A small metallic sphere of mass m and density is dropped into a tall cylinder containing a viscous liquid. Once the sphere reaches terminal velocity, the viscous force acting on it is observed to be exactly one-fourth of its weight. What is the density of the viscous liquid?

Step-by-step solution

When the sphere reaches terminal velocity, the net force acting on it is zero. This means the downward weight ( W ) is balanced by the sum of the upward buoyant force ( F_b ) and the viscous force ( F_v ). W = F_b + F_v Given that the viscous force is one-fourth of the weight ( F_v = mg 4 ): mg = F_b + mg 4 F_b = mg - mg 4 = 3mg 4 The buoyant force is also given by the weight of the displaced liquid: F_b = V g , where V is the volume of the sphere and is the density of the liquid. The volume of the sphere can be wr