Question

some leaves fall down if I vigorously shake branches of trees. why?

Answer 1

Because they were in state of rest,so when branch was shaken vigorously, they came in state of motion and the weak ones (or you can say the old ones) fell.
This is according to Newton's First Law,i.e.
Law of inertia.

Answer 2

on shaking, branches come in motion but leaves 10 to retain inertia of rest and fall.