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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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Answer» Correct Answer - 9 Side of cube `=a` `Mg=3/4a^(3)rhog` If side of cavity is `b`. New mass of cube `=(a^(3)-b^(3))3/4rho+b^(3)6/4rho=(a^(3)+b^(2))3/4rho` `a^(3)rhog=(a^(3)+b^(3))3/4rhog` `b^(3)=(a^(3))/3,b=[1/3]^(1/3)a` `b=[4/9M/(rho)]^(1/3)` |
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