Q: When a polar bear jumps on an iceberg, its weight 240 kg. wt is just sufficient to sink the iceberg. What is the mass of the iceberg ?

(specific gravity of ice is 0.9 and that of sea water is 1.02)

Sol: If M is the mass of iceberg in kg

Its Volume $\large V =\frac{M}{0.9 \times 10^3} $

The weight of displaced sea water = (V × 1.02 × 10^{3} × g) N.

$\large M g + 240 g = \frac{M}{0.9 \times 10^3} \times 1.02 \times 10^3 \times g$

$\large 240 = M (\frac{1.02}{0.9} – 1) = \frac{12}{90}M$

$\large M = \frac{90}{12} \times 240 = 1800 kg$