Question

A raft is constructed of wood having a density ρ=600 kg/ m3 Its surface area is A=5.7m² and its volume is V=0.06 m3 .When the raft is placed in fresh water of density 1 g/c m3 how much of it is below water level?
a)0.1162m b)0.03 m c) 0.059m d) 1.89m e) None of these is true

Answer 1

Mass of raft=volume*density.

Here,volume=0.06m3 and denisty=600 kg/m3

So,mass of raft=0.06*600 = 36 kg.

So, gravitational force on raft=mg, where m is mass and g is gravitational acceleration

=36*9.8 = 352.8 N.

Upward buoyant force must balance the gravitational force for equilibrium.

Now, buoyant force=weight of liquid displaced = vdg, where v is volume of displaced liquid, d is density and g is gravitational acceleration.

Volume v=A*h, where A is cross sectional area and h is the height of raft which is inside the water.

So, buoyant force=Ahdg=352.8

Here,A=5.7 m2,d=1 g/cm3=1000 kg/m3

So, 5.7*h*1000*9.8=352.8

=>h=352.8/(5.7*1000*9.8) = 0.006316 m.

So, the answer is e)none of these.