Question

A block of ice of total area A and thickness 0.5 m is floating in water. In order to just support a man of mass 100 kg, the area A should be (the specific gravity ofice is 0.9):

• A. $2.2m^2$
• B. $1.0m^2$
• C. $0.5m^2$
• D. None of these

Answer 1

Answer: (D)

None of these

Let say $m_1=$ mass of the man = 100kg
and $m_2=$ mass of the ice $=0.9\times 1000V=900V$, where $V$ is the volume of the ice block.
For equilibrium,
Total downward weight = total upthrust
$100g+900Vg=1000Vg\Rightarrow V=1m^3$
Volume = Area $\times$ height
$\Rightarrow A=\frac{Volume}{Height}=\frac{1}{0.5}=2m^2$