Question

There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the container

• A. Rises
• B. Falls
• C. Remains same
• D. Nothing can be concluded

Answer 1

Answer: (C)

Remains same

When ice with piece of metal floats,the volume V of water displaced is given by

$V=\frac{M+m}{{\rho }_w}$

where M and m are the masses of ice and metal respectively and rho is the density of water.

when the ice melts completely,then

Volume of water displaced by metal $V_1=\frac{m}{{\rho }_w}$

Volume of water due to conversion of ice into water = $V_2=\frac{M}{{\rho }_w}$

therefore, Total volume of water displaced

$V_{total}=V_1+V_2$

$=\frac{m}{{\rho }_w}+\frac{M}{{\rho }_w}$

$=\frac{m+M}{\rho \_w}$

now, $V_{total}=V$

therefore, there is no change in level of water