Question

A sphere in a liquid accelerates vertically downwards from rest. For the viscous force acting on the moving sphere, state:

a. It opposes the motion.
b. It supports the motion.
c. It is independent of velocity.
d. It causes angular acceleration.

Answer 1

The viscous force acting on a sphere moving through a liquid opposes the motion and increases with velocity, affecting linear but not angular acceleration. It plays a role in reaching a terminal velocity where it balances with gravitational and buoyant forces.

Step-by-step explanation:

When a sphere accelerates vertically downwards in a liquid, the viscous force acting on the moving sphere can be characterized as follows:

• Opposes the motion: The viscous force acts in the direction opposite to that of the sphere's motion, acting as a frictional force due to fluid viscosity.
• It is dependent on velocity: As the sphere speeds up, the flow may transition from laminar to turbulent, increasing the viscous drag force.
• It does not cause angular acceleration: The viscous force is a non-conservative force that affects the linear motion of the sphere, not its rotation.

In the context of a sphere reaching terminal velocity, the gravitational force pulling it downward is balanced by the sum of the buoyant force and the drag force, where the latter is characterized by Stokes' law.