The rod is not pinned on the vertical in a point about it rotates and thus because of the symmetry of the system (equal masses at both ends) it needs to rotate about a point situated half the distance from each end. It is just like when you set loose the rod in middle air. Because of the symmetry it has, it will start rotating about its middle point (half distance from each end). See the figure below.

Therefore as can be seen from the figure the displacement on the horizontal of the lower mass is

`x = (l/2)*cos(37) =2.5*sin(37) =1.5 m`

The correct answer choice is A) 1.5 m

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