Question

what is the scientific principle involved in beating a carpet with stick

Answer 1

This is because according to Newtons First law of motion:"The Law of Inertia"
the dust particles continue to be at rest  while beaten with stick. But while beating the carpet the carpet moves causing the dust to come out. Therefore scientific principle involved here is Law of Inertia

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Answer 2

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A body at rest remains at rest & cannot start moving on its on due to the inertia of rest.

Initially, both the carpet and the dust are at rest.

When the carpet is shaken or beaten with a stick, it is set into motion will the dust remain in the state of rest due to inertia of rest.

Thus, dust falls down due to the pull of gravity.

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