A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $F$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$\\
(1) $\frac{2}{3}\ell$\\
(2) $\frac{3}{2}\ell$\\
(3) $\frac{4}{3}\ell$\\
(4) $\ell$