Question

When a polar bear jumps on an iceberg its weight $200kg.wt$ 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 $1.02)$.

• A. $1500kg$
• B. $180kg$
• C. $1800kg$
• D. $320kg$

Answer 1

Answer: (C)

$1800kg$

$m=240kg$

Density, $\rho =s\times {10}^{3}kg/m^3$

where, $s=$ specific gravity

If M is the mass of iceberg in kg, then the volume,

$V=\frac{M}{0.9\times {10}^3}{m}^3$

The weight of displaced water, $W=V\times 1.02\times {10}^{3}kg$

From free body diagram,

$mg+Mg=Wg$

$m+M=V\times 1.02\times {10}^{3}kg$

$m+M=\frac{M}{0.9\times {10}^3}1.02\times {10}^3$

$m+M=1.133M$. . . . .(1)

$M=1800kg$

The correct option is C.