A uniform rigid meter-scale is held horizontally with one of its end at the edge of a table and the other supported by hand. Some coins of negligible mass are kept on the meter scale as shown in the figure. As the hand supporting the scale is removed, the scale starts rotating about its edge on the table and the coins start moving. If a photograph of the rotating scale is taken soon after, it will look closest to: 
The angular momentum of a particle relative to the origin varies with time (\(t\)) as \(\vec{L} = (4\hat{i} + \alpha t^2 \hat{j})\, \mathrm{kg \cdot m}^2/\mathrm{s}\), where \(\alpha = 1\, \mathrm{kg \cdot m}^2/\mathrm{s}^3\). The angle between \(\vec{L}\) and the torque acting on the particle becomes \(45^\circ\) after a time of ............ s.
