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A piece of ice is floating in a glass ve...

A piece of ice is floating in a glass vessel filled with water. How will the level of water in the vessel change when the ice melts ?

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Let m be the mass of ice piece floating in water.
In equilibrium, weight of ice piece=upthrust
or " " `mg=V_(i)rho_(w)g` or `V_(i)=(m)/(rho_(w))`
Here, `V_(i)` is the volume of ice piece immersed in water.
When the ice melts, let V be the volume of water formed by m mass of ice.
Then, " " `V=(m)/(rho_(w))`
From Eqs. (i) and (ii), we see that, `V_(i)=V`
Hence, the level will not change.
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