Horizontal component Force= Total centrifugal force acting on the rod.

Consider an element at a distance x of width dx.

$dm=\large\frac{M}{L}\;$$dx$

centrifugal force $dF=\large\frac{dmv^2}{x}$

$\qquad= \large\frac{dmx^2 w^2}{x}$

$\qquad= \large\frac{M}{l}$$ dx.xw^2$

$\therefore$ Total force $= \int \limits^l_0 \large\frac{M}{l} w^2 x dx =\large\frac{1}{2} $$Mw^2l$