Question

The density of ice is $0.92gc{m}^{-3}$ and that of sea water is $1.025gc{m}^{-3}$. The total volume of an iceberg which floats with its volume $800c{m}^3$ above water is $Xc{m}^3$. Find [$\frac{X}{1000}$].{ Where , [] is a greatest integer function}

• A. $8$
• B. $7$
• C. $6$
• D. $9$

Answer 1

The correct option is B $7$

$\frac{{vol}_{submerged}}{{vol}_{net}}=\frac{{density}_{object}}{{density}_{fluid}}=\frac{0.92}{1.025}=0.898$

$\frac{{vol}_{submerged}}{{vol}_{net}}=1-\frac{{vol}_{above}}{{vol}_{net}}$

$\frac{{vol}_{above}}{{vol}_{net}}=0.102$

=> $X={vol}_{net}=\frac{800}{0.102}=7843.13{cm}^3$
$\left[\frac{X}{1000}\right]=7$