Question

State Stoke's law for the viscous drag experienced by the spherical body falling through a

viscous liquid. Why does a spherical body achieve terminal speed? On what factors does the

terminal speed depend? Give one example each of motion around us with

(i) positive and

(ii) negative terminal velocity.​

Answer 1

Explanation:

Stokes law states that the force of viscosity on a small spherical body moving through a viscous fluid is given by:

F = 6πμrv

Where,

F ______ frictional force  acting on the interface between the fluid and the particle.  

μ ______ dynamic viscosity.

R ______ radius of the spherical object.

V ______flow velocity relative to the object.

When an object falls through a fluid, it acquires a constant velocity through its subsequent motion. This happens because the net force on the body due   to fluid and gravity becomes 0. This constant velocity is termed as terminal velocity.

The factors affecting the terminal velocity of an object are

• its mass
• its surface area
• the acceleration due to gravity ( g)

Negative terminal velocity:

When a spherical body falls through a viscous fluid, it obviously experiences a viscous force. The magnitude of viscous force increases with the increase in velocity of the falling body under the action of its weight. As a result, the viscous force soon balances the driving force and the body starts moving with a constant velocity, which is known as its terminal velocity.

In case of upward motion of sphere, terminal velocity will be negative otherwise it is positive,

Positive terminal velocity:

In case of rising bubbles in a liquid, we observe that the density of the bubble is less than the density of the enclosing liquid. So there will be an upward motion.

This indicates negative terminal velocity, as the downward direction is considered as positive.

If density of sphere is greater than the enclosing liquid, the terminal velocity will be positive.