A block of wood of volume 1000cm3 has a density of 600kgm−3. A solid cube of iron (density 7800kgm−3) is tied to the wooden block and the combination is gently released in water (density 1000kgm−3).
(a) Calculate the mass of the wooden block.
(b) If the edge length of the iron cube is xcm, express the mass of the iron cube in terms of x.
(c) Determine the maximum value of x (or, equivalently, the maximum mass of iron) that can be attached so that the wooden block and iron cube taken together just manage to float in water.