Question

An ice cube is floating in water above which a layer of lighter oil is poured. As the ice melts completely, the level of interface and the upper most level of oil will respectively:

• A. rise and fall
• B. fall and rise
• C. not change and no change
• D. not change and fall

Answer 1

The correct option is A rise and fall

When ice melts into water its volume decreases. Hence over all level should decrease.
Now suppose m is the mass of ice, $V_1$ is volume immersed in water and $V_2$ the volume immersed in oil. Then in floating condition,
weight=upthrust
$\therefore$ $mg=V_1{\rho }_{w}g+V_2{\rho }_{0}g$
$\therefore$ $V_1=\frac{m-V_2{\rho }_0}{{\rho }_w}=\frac{m}{{\rho }_w}-\frac{V_2{\rho }_0}{{\rho }_w}$
(i)
When ice melts, m mass of ice converts into m mass about of water. Volume of water so formed is
$V_3=\frac{m}{{\rho }_w}$

(ii)
From Eqs. (i) and (ii), $V_3>V_1$
$\therefore$ Interface level will rise.