res. sir

i want ask , what general method is used to calculate either water level will rise or fall in the following cases:

1)an ice is floating in tub of water. after complete melting will water level rise or fall?

2)same as previous question but this time with a cork inside ice cube?

3)same as 1) but this time a lead ball inside ice cube?

4)_a person drink water from a pond in which he was floating on a boat, whether water level of pond will rise or fall?

i am really thankful for any sought of help provided by you

yours sincerely

AMANPREET

Dear aman,

Water expands when it freezes, so you might think that when it melts and reduces in size, the water level will go down. Alternatively, because part of the ice floats the water, you might think that when it melts, the water level will rise.

Neither is true, as explained by Archimedes principles.

When an ice cube (or an iceberg, which is a big ice cube) floats in water, then by definition the weight of the ice cube is exactly equal to the buoyancy force, which is equal to the weight of the displaced water.

When the ice cube melts, its volume changes, but its weight is conserved (law of the conservation of mass). So the melted water from the ice cube has exactly the same weight as the water that was displaced by the ice cube when it was frozen -- therefore the volume of melted water fits exactly in the previously displaced volume -- and the water level stays the same.

Note that this argument applies only if the ice cube is made of the same water as the water that it is floating in. This is true, for example, with the Arctic ice pack, which is made of frozen sea water. However, it is not true for Antarctic icebergs, which are blocks of fresh-water ice from the continent that are floating in salt-water sea. In this case, we must take into account that the salt water is denser than the fresh water. The fresh-water iceberg still weighs as much as the weight of the displaced salt water, but because of the difference in density, the volume of melted fresh water will be slightly greater than the displaced volume of salt water -- so when the iceberg melts, the water level will rise, although the difference is very small.

Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.

All the best.

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