Problem 1.234

A thin uniform rod $A B$ of mass $m=1.0 \mathrm{~kg}$ moves translationally with acceleration $w=2.0 \mathrm{~m} / \mathrm{s}^{2}$ due to two antiparallel forces $\mathbf{F}_ {1}$ and $\mathbf{F}_ {2}$ (Fig. 1.52). The distance between the points at which these forces are applied is equal to $a=20 \mathrm{~cm} .$ Besides, it is known that $F_{2}=5.0 \mathrm{~N} .$ Find the length of the rod.