Q2 of 81 Page 225

Four particles having masses m, 2m, 3m and 4m are placed at the four corners of a square of edge α. Find the gravitational force acting on a particle of mass m placed at the center.

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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