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A uniform cube of mass M is floating on ...

A uniform cube of mass `M` is floating on the surface of a liquid with three fourth of its volume immersed in the liquid (density of liquid is `rho`). Now a cubical cavity is made inside the cube and the cavity is filled by a material having twice the density of the original cube. The minimum dimension (sides) of this cavity such that this cube is now completely immersed in the liquid is `[(4M)/(nrho)]^(1/3)`. Find the value of `n`

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