Three particles A, B and C, each of mass m, are connected to each other by three massless rigid rods to form a rigid equilateral triangular body of side l. This body is placed on a horizontal frictionless table and is hinged to it at the point A, so that it can move without friction about the vertical axis through A. The body is set into rotational motion on the table about A with a constant angular velocity `omega`. Find the magnitude of the horizontal force exerted by the hinge on the body.