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A uniform rod of mass \( m \) and length \( l \) is placed over a smooth horizontal surface along the \( y \)-axis and is at rest as
\( \mathrm{P} \) shown in figure. An impulsive

W force \( F \) is applied for a small time \( \Delta t \) along \( x \)-direction at point \( A \). The \( x \)-coordinate of end \( A \) of the rod when the rod becomes parallel to \( x \)-axis for the first time is [initially, the coordinate of centre of mass of the rod is \( (0,0) \) ]
(1) \( \frac{\pi l}{12} \)
(2) \( \frac{l}{2}\left(1+\frac{\pi}{12}\right) \)
(3) \( \frac{l}{2}\left(1-\frac{\pi}{6}\right) \)
(4) \( \frac{l}{2}\left(1+\frac{\pi}{6}\right) \)
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