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A T shaped object with dimensions shown in the figure , is lying on a smooth floor. A force \vec{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

A.      \frac{4}{3}l

B.        l

C.      \frac{3}{4}l

D.      \frac{3}{2}l

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\\\text{It is a case of translation motion without rotation. } \\ \text{The force should act at the center of mass }\\\\ \mathrm{T}_{\mathrm{cm}}=\frac{(\mathrm{m} \times 2 \mathrm{l})+(2 \mathrm{m} \times \mathrm{l})}{\mathrm{m}+2 \mathrm{m}}=\frac{4 \mathrm{l}}{3}

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