Question

When a polar bear jumps onto an iceberg, its weight 200 kg.wt. is just sufficient to sink the iceberg. Then the weight of ice-berg is (specific gravity of ice = 0.9; Sp.gr. of sea water = 1.02)

Answer 1

The specific gravity of ice = 0.9.
The specific gravity of sea water = 1.02.
Let 'M' be the weight and v be the volume of an iceberg.
According to the Archimede's Principle,
$M\times g+200=p\left(water\right)\times g\times V$ (1)
Where p(water) is the density of water
As, $V=\frac{M}{p\left(ice\right)}$
where p(ice) is the density of ice
$M+200=\frac{p\left(water\right)\times M}{p\left(ice\right)}$
Therefore,
$M=\frac{200}{g\times \{\frac{p\left(water\right)}{p\left(ice\right)}-1\}}=\frac{200}{10\times \{\frac{1.02}{0.9}-1\}}$
$=\frac{200}{10\times 0.13}$
$=153.8461\simeq 1500$