An isosceles right angled tunnel ABO is made inside the earth from surface of earth to its centre as shown in the figure. The distance between the points A and B and that between the points B and O is $\frac{R}{\sqrt{2}}$, where R is the radius of earth. The surface of tunnel is assumed to be frictionless. A small particle of mass $m_0$  is released from point A. The collision between the particle and the tunnel is assumed to be perfectly inelastic. Take mass of earth as M, Radius of earth R=6400 km and $g=10m/s^2$ . The time taken by the particle to move in the tunnel from A to O is n x100$\pi$ sec. Find n.