One end of a long iron chain of linear mass density  $\lambda$ is fixed to a sphere of mass  m and specific density 1/3  while the other end is free. The sphere along with the chain is  immersed in a deep lake. If specific density of iron is 7, the height  h above the bed of the lake at which the sphere will float in equilibrium is $\frac{xm}{\lambda }.Find x.$

 (Assume that the part of the chain lying on the bottom of the lake exerts negligible forces on the upper part of the chain)