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Newton's law is valid only in inertial object of reference. For the validity of Newton's law we require the concept of pseudo force.
Let us take an example in which an object is placed on a smooth horizontal surface and two observers B and A are observing the same block.
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Observer A is fixed and observer B is moving with acceleration (a) towards the +ve X direction. A will see that the acceleration of block is zero and no force is acting on the block and hence Newton's law is not correct. To create Newton's law valid observer B will give a hypothetical force on block having value m x. Acceleration of observer B is in the direction reverse to the direction of observer B. This hypothetical force is known as pseudo force.
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So free object diagram of body according to observer B.
Fpseudo = ma
It is very important to observe that pseudo force will only apply for the observer who is observing the motion from the non inertial frame of reference.
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