Question

A wooden cube of side 10 cm has mass 700 g. What part of it remains above the water surface while floating vertically on water surface? 

Answer 1

Given, Side of wooden cube = 10 cm

Hence, Volume of wooden cube = 10 cm × 10 cm × 10 cm = 1000 cm³

Mass = 700 g

Density = `"mass"/"volume"`

∴ Density of wooden cube = `700/1000` = 0.7 g cm^-3

By the principle of floatation,

`"Volume of immersed part"/"Total volume" = "Density of wood"/"Density of water"`

Density of water = 1 g cm^-3

Density of wooden cube = 0.7 g cm^-3 

∴ `"Volume of immersed part"/"Total volume" = 0.7/1`

Hence, fraction submerged = 0.7

Height of wooden cube = 10 cm

Part of wooden cube which is submerged = 10 x 0.7 = 7 cm

Therefore, part above water = 10 - 7 = 3 cm

Hence, 3 cm of height of wooden cube remains above water while floating.