Alog floats in a river with one-forth of its volume about the water. (a) what is the density of the log?

This problem can be solved by using the Archimedes Principle. The principle basically lets us derive a force balance between the weight of the log and the buoyant force exerted by the water, that is

weight of log = buoyant force exerted by water

simplification of the derviation would yield,

Dl/Dw = fraction of the of the log submerged in water = (1-0.25) = 0.75

where Dl = density of the log
Dw = density of the water (1000 kg/m3)

therefore Dl = 750 kg/m^3

Hope this helps 

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