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# Ice cube of size $100\;cm$ and area of base $(500 m \times 50 m)$ is floating in a tank partially filled with water. The change in gravitational potential energy, when ice melts completely (density of Ice is $900\;kg/m^3$)

$(a)\;-0.072\;J \quad (b)\;-0.24\;J \quad (c)\;-0.016\;J \quad (d)\;-0.045\;J$

Relative density of ice is 0.9. Hence $90\%$ of volume of ice is immused in water.
When ice melts completely level of water does not change
Therefore the change in $CG=GG'=0.5\; cm$
Change in potential energy
$\Delta V=-mgh$
$\qquad=-(0.1)^3(900)(10)(0.5 \times 10^{-2})J$
$\qquad=-0.045\;J$
Hence d is the correct answer.

edited Feb 10, 2014 by meena.p