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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

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

The correct option is D Remains same
When ice with piece of metal floats,the volume V of water displaced is given by
V=M+mρw
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 V1=mρw
Volume of water due to conversion of ice into water = V2=Mρw
therefore, Total volume of water displaced
Vtotal=V1+V2
=mρw+Mρw
=m+Mρ_w
now, Vtotal=V
therefore, there is no change in level of water

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