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What is the maximum length of a body floating vertically in water?

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Maximum length of a body floating vertically in water

We see that a cube of wood (having specific gravity less than unity can float in water, in any position. If we maintain any two sides (say breadth and thickness), of the cube, constant and go on gradually increasing the third side (say length) and try to float the block vertically in water, we see that the block can float vertically in water up to some length. If we increase the length of the block, beyond this length, we find that it cannot float vertically in water; through it can float longitudinally.

This maximum permissible length of the block, floating vertically in water, may be found out by keeping the body in stable equilibrium. Or in other words, this can also be found out by avoiding the unstable equilibrium of the floating body. For doing so, the metacentre (M) should be above centre of gravity (G) of the floating body (a condition of stable equilibrium) or the metacentre (M) may coincide with the centre of gravity (G) of the floating body (a condition of neutral equilibrium i.e., by avoiding the unstable equilibrium).

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