Question

the principle involved in the dusting of a carpet

Answer 1

Beating of a carpet with a stick; makes the carpet come in motion suddenly, while dust particles trapped within the pores of carpet have tendency to remain in rest, and in order to maintain the position of rest they come out of carpet. This happens because of the application of Newton’s First Law of Motion which states that any object remains in its state unless any external force is applied over it.
The principal follows the first law of motion

Answer 2

The principle which is involved in dusting of a carpet is the FIRST LAW OF MOTION.
Initially both the carpet and the dust particles are at rest.
When v beat the carpet it comes into motion.
But the dust particles continue to be in their inertia of rest and gets detached from the carpet.