Question

What is terminal velocity? What are the factors on which terminal velocity depends?

Answer 1

Hint: The constant value of speed that a freely falling body acquires when the resistance of the medium through which its falling prevents further acceleration of the body, is termed as terminal velocity of the body. So as to calculate the terminal velocity of a body during a liquid of density, we would like to apply Stoke’s law and balance the downward gravitational force of the body with the sum of upthrust and viscous force acting on the body.

Complete step-by-step solution:
Terminal velocity is termed as the highest velocity attained by a body that’s falling through a fluid. It’s observed when the sum of drag force and buoyant force becomes adequate to the downward gravitational force that’s acting on the body. The acceleration of the body is zero because the net force acting on the body is zero.
Viscous drag or a viscous force acts in the direction opposite to the motion of the body within the fluid. Consistent with stoke’s law, the magnitude of the opposing viscous drag increases with the increasing velocity of the body.
As the body falls through a medium, its velocity goes on increasing because of the force of gravity acting on it. After that, the opposing viscous or drag force, which acts upwards, also goes on increasing. A stage reaches when the true weight of the body is simply equal to the sum of the upward thrust because of buoyancy, that is, upthrust, and also the upward viscous drag. In this situation, there is no net force to accelerate the moving body. Hence it starts falling with a constant velocity, which is named terminal velocity.
The terminal velocity acquired by the ball of the radius \[r\]when dropped through a liquid of viscosity \[\eta \] and density\[\rho \].
\[v = \dfrac{{2{r^2}\left( {{\rho _0} - \rho } \right)g}}{{9\eta }}\]
Hence, terminal velocity depends on object radius, coefficient of viscosity of the medium, object density, density of the medium.

Note: Terminal velocity is called the maximum velocity attained by a body because it falls through a fluid. It occurs when the sum of the drag force and also the buoyancy, is adequate to the downward gravitational force acting on the body. Since the net force on the body is zero, the body has zero acceleration. The terminal speed is directly proportional to the square of the body radius and inversely proportional to the coefficient of viscosity of the medium. It also depends upon the densities of the body and also the medium.