Physics 2009 JAMB Past Questions - Question 13: The terminal velocity from a ball-bearing falling through a viscous fluid is reached when the

Correct Answer

D

Explanation

Terminal velocity is the constant velocity that a falling object reaches when the force of gravity pulling it downward is balanced by the resistive force of the medium (in this case, a viscous fluid) through which it is moving. In the case of a ball-bearing falling through a viscous fluid, several factors determine when terminal velocity is reached:

1. **Gravity:** The gravitational force pulls the ball-bearing downward. Initially, the ball-bearing accelerates due to gravity.

2. **Viscous Drag:** As the ball-bearing moves through the viscous fluid, it experiences a drag force in the opposite direction of its motion. The magnitude of this drag force is determined by the shape and size of the ball-bearing, as well as the viscosity of the fluid.

3. **Velocity:** The terminal velocity is reached when the drag force becomes equal in magnitude to the gravitational force acting on the ball-bearing. At this point, there is no net force, so the ball-bearing stops accelerating and falls at a constant velocity.

The key point is that the terminal velocity is reached when the net force on the ball-bearing is zero. This occurs when the gravitational force (mg, where m is the mass of the ball-bearing and g is the acceleration due to gravity) is balanced by the viscous drag force (F_drag). Mathematically, this can be expressed as:

**mg = F_drag**

The expression for viscous drag depends on the shape and size of the object and the properties of the fluid. For spherical objects like a ball-bearing moving through a viscous fluid, the drag force can be approximated by Stokes' law:

**F_drag = 6πηrv**

Where:
- η is the dynamic viscosity of the fluid.
- r is the radius of the ball-bearing.
- v is the velocity of the ball-bearing.

As the ball-bearing falls and accelerates, its velocity increases. The drag force also increases with velocity, eventually becoming equal to the gravitational force. At this point, the ball-bearing reaches its terminal velocity, and it continues to fall at a constant speed because there is no net force acting on it.

The time it takes to reach terminal velocity can vary depending on factors such as the initial conditions (e.g., height from which the ball-bearing is released), the properties of the fluid, and the size and shape of the ball-bearing. Once terminal velocity is reached, the ball-bearing will maintain a constant speed as long as the conditions remain constant.