Question

A wooden cube of side 10 cm has a mass of 700 g. It will float in the water with:
(a) Half of its volume inside the water
(b) 3 cm height above the water surface
(c) 7 cm height above the water surface
(d) Just inside the water surface.

Answer 1

Side of wooden cube = 10 cm.
Volume of wooden cube = 10 × 10 × 10 = 1000 cm³.
Mass of wooden cube = 700 g.
Density of wooden cube = mass/volume = 700/1000 = 0.7 gcm^-3.
Density of water = 1 gcm^-3.
(Density of floating body / Density of liquid) = fraction submerged
0.7/1 =fraction submerged
The fraction of wooden cube submerged in water = 0.7
Height of wooden cube = 10 cm
Part of wooden cube which is submerged = 10 × 0.7 = 7 cm
So, a wooden cube will float in the water with a 3 cm height above the water surface.