Question

A glass of water has an ice cube floating in the water. The water level just touches the ring of the glass. Will the water overflow when the ice melts? Give reason.

Answer 1

Hint: The density of ice is less than the density of water. This is due to the anomalous expansion of water. According to this property, water expands instead of contracting when it is cooled to a temperature below ${4^ \circ }C$. Hence volume increases and density decreases on cooling.
An object floats in the water when the weight of the body is balanced by the upthrust produced by the water. So here the weight of ice is balanced by the force of upthrust.
When an ice cube is in water it displaces a volume of water equal to its volume.

Complete answer:
An object floats in the water when the weight of the body is balanced by the upthrust produced by the water. So here the weight of ice is balanced by the force of upthrust.
When an ice cube is in water it displaces a volume of water equal to its volume.
The density of ice is less than the density of water. This is due to the anomalous expansion of water. According to this property, water expands instead of contracting when it is cooled to a temperature below ${4^ \circ }C$. Hence volume increases and density decreases on cooling.
Ice has already displaced water equal to its volume which is greater than the volume of water it will produce on melting. So even if it melts it is not going to raise the water level and hence the water in the glass will not overflow.

Therefore, When the floating ice cube melts the water level in the glass will not rise.

Additional information:
Anomalous expansion of water is the reason why aquatic life can survive underwater in cold countries. When the surrounding temperature decreases the upper layer of the lakes in cold countries starts cooling. Due to cooling its volume decreases and density increases. Due to the increase in density the water in this layer starts sinking towards the bottom. Then the new layer that forms on the top starts cooling and again due to an increase in density it will sink. This process continues until the entire layer of water is cooled to ${4^ \circ }C$. Below ${4^ \circ }C$ water starts expanding instead of contracting due to its property anomalous expansion. Hence the layer on the surface now starts to expand and its density decreases. Since the density of this layer is now less than that of the lower layers it will stay on the top and undergo further cooling. When it reaches ${0^ \circ }C$ it becomes ice. Since ice is a bad conductor of heat. The lower oven will not be cooled further. Thus, even though the surface of the lake is entirely converted into ice the lower layers will still remain at ${4^ \circ }C$. This helps aquatic animals and plants to survive underwater.

Note:
All substances contract on cooling. So when they melt the volume will increase. But this is not the case with water below ${4^ \circ }C$. Due to the anomalous expansion of water ice has more density than that of water. When it melts volume is decreasing so the water level in the glass will decrease. This property is shown only below ${4^ \circ }C$ until it reaches this temperature water also contracts on cooling like other substances.