Question

why does the dust particles come out when carpet is beaten with a stick ??

Answer 1

This phenomenon is a simple law of inertia.
Inertia is the property of body by virtue of which a body tends to remain in its position of rest or motion.
So is this case in which when we beat the carpet with stick we set the carpet in motion in air while the dust particles due to their property of inertia tend to remain at rest (since initially they were at rest),and get seperated from the carpet. 
Now some of you may think that why doesn't the carpet shows the property of inertia in this case,it's because when we beat it with stick we apply external force on it while law of inertia holds good only in the absence of any external force. 
Hope my answer was helpful....

Answer 2

Answer:

1. When a carpet is beaten with a stick, the force makes the particles of carpet move.
2. When a carpet is beaten with a stick, the force makes the particles of carpet move.But the dust particles remain at rest due to the property of inertia.
3. As such the properties of test and separated from the material of carpet and so the dust comes out of it.