Question

When a metallic sphere is dropped in a long column of a liquid, the motion of the sphere is opposed by the viscous force of the liquid. If the apparent weight of the sphere equals to the retarding forces on it, the sphere moves down with a velocity called:
A. critical velocity
B. terminal velocity
C. velocity gradient
D. constant velocity

Answer 1

Velocity determines the speed and direction of an object.The apparent weight of the sphere is the difference of its weight and upward buoyant force. The velocity of a body depends on its viscous force.

Complete step by step answer:
When a metallic sphere is dropped in a long column of a liquid, three forces act on it: the buoyant force, viscous force, and the force due to gravity. The buoyant force and viscous force are acting upward and the weight actin upward’
The viscous force is obtained from Stock ‘law, Stoke's Law is a mathematical equation. The law is derived considering the forces acting on a particle as it sinks through the liquid column under the influence of gravity. The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere, and the viscosity of the fluid. The viscous force is expressed as,
${{F = }}\,\,{{6\pi \eta rv}}$
$\left( {{r}} \right)$ is the radius of the sphere, $\left( {{\eta }} \right)$ is the coefficient of viscosity, $\left( {{v}} \right)$ is the velocity of the object.
When the ball the sphere moves downwards, the velocity increases and this increases the viscous force acting on it. Since the apparent weight of the sphere equals to the retarding forces on it, the sphere after some time the viscous force equals to the net force that is,
${{mg - }}{{{F}}_b}{{ = }}\,\,{{{F}}_v}$
Therefore, the ball moves with a constant velocity called its terminal velocity.

So, the correct answer is Option B.

Note: Terminal velocity, steady speed achieved by an object freely falling through a gas or liquid.
Critical velocity is defined as the speed a falling object reaches when both gravity and air resistance are acting equal on the object. It indicates the directions and speed of the object. It is depending upon the viscosity and density of the liquid.