Hello,

If the table was rough i.e. had friction, the static friction force would have adjusted itself to match the external force F and hence two equal and opposite forces would have caused stress to occur in the rod. But here the table is smooth, so I don't know what other force will oppose the external force and how stress will be produced.

I'm not sure of this but if I assume that atomic force of attraction would oppose the external force and the rod is reduced to the center of mass(at a distance of l2l2 ), the following strain energy would be stored in the rod:-

U=12Y(stress)2Al2U=12Y(stress)2Al2

U=12Y(FA)2Al2U=12Y(FA)2Al2

U=F2l4YA

Hope this helps, Good luck.