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A glass of water has an ice cube floatin...

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

Text Solution

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Let Mg of ice be floating in water of density 1g/`cm^(3)`
Then from the law of floatation,`M=Vrho_(ice)=V_("im" rho "water")`
`therefore V_(im)Mcm^(3)to` (Volume of water displaced)…..(i)
Now, if the entire ice melts, water formed will have same mass M but the volume
`V_("formed")=(M)/(rho_("water"))=Mcm^(3)` ......(ii)
From (i) and (ii) volume of water displaced is equal to volume of water formed due to melting of ice. Therefore, the level of water remains unchanged.
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