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Question

A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9.


Solution

Given:
Specific gravity of ice, ρice = 0.9 gm/cc
Weight of the metal piece, m = 5 kg
Density of water, ρw = 103 kg/m3
Let x be the minimum edge of the ice block in cm.
We have:
mg + Wice = U
Here,
U = Upward thrust
Wice = Weight of the ice
Thus, we have:0.5×g+x3×ρice×g=x3×ρw×g      Volume of the liquid displaced=x30.5×103+x3×(0.9)=x3×1x3×(0.1)=(0.5)×103x3=5×103x=17.09 cmx=17 cm

Physics
HC Verma - I
Standard XI

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