A spherical body is allowed to fall through a long column of a highly viscous liquid. Which of the following describes the correct graph showing how the terminal velocity ( v_t ) plotted on the y-axis varies with the radius of the body ( r ) plotted on the x-axis?

Step-by-step solution

The terminal velocity v_t of a spherical body of radius r falling through a viscous liquid is given by: v_t = 2 9 ( - ) r^2 g Since the density of the body ( ), the density of the liquid ( ), and the viscosity of the liquid ( ) are constant for a given material and liquid, we have: v_t r^2 This relationship is of the form y = kx^2 , which represents a parabola opening upwards (along the positive y-axis). Therefore, the graph of terminal velocity ( v_t ) versus radius ( r ) is a parabola opening along the positive v