Answer :
The gravitational force at the center is equal to the vector sum of all the forces acting on it.
The distance between the center particle with others, ![]()

The force acting between particles of mass m and center particle is ![]()
The force acting between particles of mass 2m and center particle is ![]()
Similarly,
between particles of mass 3m and center particle is ![]()
And between particles of mass 4m and center particle ![]()

Cancelling out the vertical and horizontal components, the net force is
![]()
![]()
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