Question

What is the area of the smallest block of ice $0.5m$ thick that will just support a man of mass $100kg$ ? The block of ice is floating in fresh water. (Given: specific gravity of ice $=0.9$)

• A. $3m^2$
• B. $2m^2$
• C. $1m^2$
• D. $5m^2$

Answer 1

The correct option is B $2m^2$

Given, mass of man, $m=100kg$
Specific gravity of ice,

$\frac{p_{ice}}{p_{water}}=0.9$

$p_{ice}=0.9\times 1000=900kg/m^3$

Thickness of ice block $=0.5$
Let the area of the ice block be $A$.
So, volume of the ice block,

$V=A\times 0.5$

Equating upthrust with the total weight to be supported,

$A\times 0.5\times 1000g=100g+A\times 0.5\times 900g$

$500A=100+450A$

$A=2m^2$