If we consider a free falling body and the Earth as the system, then the gravity is an internal force and there are no other external forces acting on the body. Then how do we explain the displacement of the centre of mass of the body as we know only external forces can displace the centre of mass ?

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    $\begingroup$ Since the Earth is part of the system you have to also take into account the mass of the Earth when computing the center of mass. This combined center of mass will not accelerate since the force of the Earth pulling the body is equal but opposite to the force that the falling body is exerting on the Earth. $\endgroup$ – AccidentalTaylorExpansion Sep 2 '17 at 14:45
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    $\begingroup$ @user3502079 That sounds like an answer. $\endgroup$ – garyp Sep 2 '17 at 14:53

When a body moves towards earth due to gravitational force, an equal amount of force acts on earth too which causes not only the body to move towards the earth but also the earth towards the body but with negligible speed (because of negligible mass of body as compared to earth). All this happens such that the centre of mass of earth-body system doesnt get displaced because no external force acts on the system . So, basically, the center of mass remains undisplaced because both the body and earth move towards each other because of their gravitational force (internal force).

  • $\begingroup$ Then that means if we increase the number of elements in our system, then the number of external forces reduce? $\endgroup$ – Hardik Raj Sep 3 '17 at 3:58
  • $\begingroup$ @hardik i did'nt get you. can you give an example? $\endgroup$ – Ayush Raj Sep 3 '17 at 7:34
  • $\begingroup$ Suppose a block B is kept over a block A having friction and the block A is kept on on rough surface. If we consider the two blocks as a system then the friction between block A and ground is an external force along with the gravitational force. But we include the earth in the system also then there are no external forces . $\endgroup$ – Hardik Raj Sep 4 '17 at 16:44
  • $\begingroup$ @HardikRaj if you consider the 2 blocks as a system, the frictional force acting on the system as well as the gravitational force are external forces for the centre of mass. But if you consider the 2 blocks and the earth as a system, then only those forces are considered on the centre of mass of the system which acts externally on it. $\endgroup$ – Ayush Raj Sep 6 '17 at 16:01

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