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Question
An apple falls from a tree. An insect in the apple finds that the earth is falling towards it with an acceleration g. Who exerts the force needed to accelerate the earth with this acceleration g?
Solution
The mutual gravitational force between the apple and the Earth is responsible for the acceleration produced in the apple falling from the tree. Although the Earth will experience the same force, it does not get attracted towards the apple because of its large mass. The insect feels that the Earth is falling towards the apple with an acceleration g because of the the relative motion.
let
vae = velocity of apple w.r.t earth
\[V_{ea} = \text {velocity of earth w . r . t apple }\]
\[v_{ae} = v_a - v_e = - ( v_e - v_a ) = - v_{ea}\]
As the insect is in the frame of apple so he sees the earth moving with a relative velocity \[v_{ea}\].
Any other observer on earth will see the apple moving towards earth with velocity \[v_{ae}\].
Both are opposite in direction.
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