A $T$ shaped object with dimensions shown in figure, is lying on a smooth floor. A force $\overrightarrow{F}$ 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 $C$: <br>

Question

( A ) $\frac{4}{3}l$
( B ) $\frac{3}{2}l$
( C ) $\frac{2}{3}l$
( D ) $l$