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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.
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Solution
Given:
Specific gravity of ice, ρice = 0.9 gm/cc
Weight of the metal piece, m = 500 g
Density of water, \[\rho_w\] = 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
\[\text{Thus, we have: }\]
\[0 . 5 \times \text{ g + x}^3 \times \rho_{\text{ ice }} \times \text{ g = x} ^3 \times \rho_w \times g \left[ \text{ Volume of the liquid displaced = x}^3 \right]\]
\[ \Rightarrow 0 . 5 \times {10}^3 + x^3 \times (0 . 9) = x^3 \times 1\]
\[ \Rightarrow x^3 \times (0 . 1) = (0 . 5) \times {10}^3 \]
\[ \Rightarrow x^3 = 5 \times {10}^3 \]
\[ \Rightarrow x = 17 . 09 \text{ cm}\]
\[ \Rightarrow x = 17 \text{ cm }\]
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