A piece of wood is floating at the surface of some water as

A piece of wood is floating at the surface of some water as illustrated. The wood has a circular cross section and a height h = 3.0 cm. The density of the wood is 0.41 g/cm^3. The distance y from the surface of the water to the bottom of the wood is impossible to determine because the area of the cross section is not given. 0.81 cm 3.2 cm 1.2 cm None of these is correct.

Solution

Density of solid / density of liquid = submerged volume / solid volume

(0.41 g/cm ³ ) / (1 g / cm ³ ) = (Area of cross section) y / ( Area of cross section ) h

Since volume = Area of crosssection x height

Both the crosssectional areas are same.

(0.41 g/cm ³ ) / (1 g / cm ³ ) = y / h

From this y = h [(0.41 g/cm ³ ) / (1 g / cm ³ ) ]

                 = (3 cm) ( 0.41)

                = 1.23 cm

               = 1.2 cm           ( two significant figures0