Question

An ice cube is floating in water above which a layer of a lighter oil is poured. As the melts completely, the level of water surface (or interface) and upper level of oil will

• A. rise and fall
• B. fall and rise
• C. not change and change
• D. not change and not fall

Answer 1

The correct option is A rise and fall

As ice melts ,its volume decreases so oil level will decrease ,and as volume of water increases ,so level of interface will increase

When ice melts into water its volume decrease.

Hence, over all level should decrease.

Now suppose$m$ is the mass of ice

is

$V_1$ volume immersed in water and $V_2$ the volume immersed in oil.

Then in floating condition, weight=upthrust

$\therefore mg=\left(V_1\right)\left({\rho }_w\right)g+\left(V_2\right)\left({\rho }_0\right)g$

$V_1=\frac{m-V_2{\rho }_0}{{\rho }_w}$

$V_1=\frac{m}{{\rho }_w}-\frac{V_2{\rho }_0}{{\rho }_w}$

When ice melts, m mass of ice converts into m mass of water. Volume of water so formed is :

$V_3=\frac{m}{{\rho }_w}$

From eq:-

$V_3>V_1$

Interface level is rise.