A solid sphere attains a constant terminal velocity while falling through a viscous liquid. It is observed that the viscous drag force acting on the sphere is k times the buoyant force exerted by the liquid. The ratio of the density of the sphere's material to the density of the liquid is:

Step-by-step solution

Let the volume of the sphere be V , the density of the sphere's material be , and the density of the liquid be _l . The weight of the sphere is W = V g . The buoyant force is B = _l V g . At constant terminal velocity, the net force on the sphere is zero. Therefore, the downward weight is balanced by the upward buoyant force and the viscous drag force F_v . W = B + F_v It is given that F_v = k B . Substituting this into the force balance equation gives: W = B + k B = B(k+1) Substituting the expressions for W and B