A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density $0.8$ and with its vertex submerged. When another liquid of relative density $\rho$ is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is $0.10$ $m$ and the radius of the circular base is $0.05$ $m$. The specific gravity $\rho$ is given by
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