Question

why do the dust particle fall from the beaten cloth

Answer 1

due to law of inertia...
when the cloth is beaten the dust particles remains at rest due to inertia of rest...
and there for they fall down

Answer 2

To clarify the above answer:
When we beat the cloth the dust particles remain in their position and the cloth moves forward. So the dust comes out and fall down...... This is the first situation.
The dust particles being lighter move more than the beaten cloth. So they move out and float down........  This the second situation.