Some leaves of the trees get detached from a tree when we shake their branches vigorously because when we shake the branches, the branches come in motion, while the leaves tend to remain at rest due to the inertia of rest.
When the tree is at rest, that means, its leaves are also at rest. But when we bring the tree in motion by means of shaking it, due to the inertia of leaves they still tends to be in rest.
That is, the force is acting on leaves vigorously with changing direction rapidly. This result in detaching of leaves from the leaves.
Inertia of rest is defined as the fundamental property of a body to oppose any change in its state of rest. Or we can say that body does not want to change its state of rest, but wants to continue its state of rest.
To learn more about inertia of rest here
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