A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses  $\left(\frac{m}{M}\right)$ is $\frac{1}{x}$ . The value of $x$ will be….