That will depend on the distance between the points where the beam is supported, as well as the type of wood.
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Only if it is at least 12' long.
It would depend on the type of paper as well as the thickness. For example, wood pulp paper would weigh much more than rice paper.
Capacity is referring to volume, not weight. Weight is the force of gravity acting on an object. 1 pound of lead and one pound of wood have the same weight (1 lb) but they have very different volumes (capacities).
-- The aggregate density of the wood block is 700/1000 = 0.7 the density of water. -- So, as soon as the wood has displaced 0.7 of its volume in water, it has displaced its entire weight in water, and floats. -- The wood floats with 0.7 of its volume below the surface and 0.3 of its volume above it.
That would depend on the thickness of the plank. It would also vary, depending on the type of wood, and where you buy it (what country, for instance).