Question

An ice cube of size $a=10cm$ is floating in a tank (base area $A=50cm\times 50cm$) partially filled with water. The change in gravitational potential energy when ice melts completely is
(density of ice is $900kg/m^3$):

• A. $-0.072J$
• B. $-0.24J$
• C. $-0.016J$
• D. $-0.0045J$

Answer 1

Answer: (D)

$-0.0045J$

The volume of the ice cube is 0.001 $m^3$ so the mass of the ice is $0.001\times 900=0.9kg$

So when after melting, the Ice become water the volume will be $\frac{0.9}{1000}=0.0009kg$

So the excess volume of the cube that was above the water is $0.001-0.0009$ = $0.0001m^3$

after the ice becomes water it will fit into the volume that was inside the water and hence the change in the potential energy will for the portion that was outside the water. The height of the portion is $\frac{0.0001}{0.001}=0.01m$

Now the potential energy for a rectangular slab of height h and area A is $P=A\rho g\frac{h^2}{2}$

Putting the values of the parameter we get $P=0.001\times 900\times 9.8\times \frac{{0.01}^2}{2}=0.0045$

Hence potential energy will be reduced by $0.0045J$