When a tree is vigorously shaken, the branches of the tree come in motion but the leaves tend to continue in their state of rest due to inertia of rest. As a result of this, leaves get separated from the branches of the tree and hence fall down.
When a tree is vigorously shaken, the branches of the tree come in motion moving left and right and shake the leaves off, that's why some of the tree got detached when we vigorously shake its branch.
