A non uniform cube of side length \( a \) is kept inside a container as shown in the figure. The...

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A non uniform cube of side length \( a \) is kept inside a container as shown in the figure. The average density of the material of the cube is \( 2 \rho \) where \( \rho \) is the density of water. Water is gradually filled in the container. It is observed that the cube begins to topple, about its edge (into the plane of the figure) passing through point \( A \), when the height of the water in the a container becomes \( \frac{a}{2} \). Find \( N \) if the distance of the centre of mass of the cube from the face \( A B \) of the cube is \( a / N \). Assume that water seeps under the cube.
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