A rod $\mathrm{P}$ of length $1 \mathrm{m}$, is hinged at one end $\mathrm{A}$ and there is a ring attached to the other end. Another long rod $\mathrm{Q}$ is hinged at $\mathrm{B}$ and it passes through the ring. The rod $\mathrm{P}$ is rotated about an axis which is perpendicular to the plane in which both rods are present and the variations between the angles $\mathrm{\theta }$ and $\varphi$ are plotted as shown.The distance between the hinges $\mathrm{A}$ and $\mathrm{B}$ is