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 (x-y plane) and is hinged at point A so that it can move without friction about the vertical axis through A (see figure). The body is set into rotational motion on the table about this axis with a constant angular velocity . (a) Find the magnitude of the horizontal force exerted by the hinge on the body. (b) At time T, when side BC is parallel to the x-axis, force F is applied on B along with BC (as in the figure). Obtain the x-component and the y-component of the force exerted by the hinge on the body, immediately after time T.
