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. 

Answer 1

Given:
Specific gravity of ice, ρ_ice = 0.9 gm/cc
Weight of the metal piece, m = 500 g
Density of water,  \[\rho_w\] = 10³ kg/m^3​

Let x be the minimum edge of the ice block in cm.
We have:
mg + W_ice = U 
Here,
U = Upward thrust
W_ice = Weight of the ice

\[\text{Thus, we have: }\]

\[0 . 5 \times \text{ g + x}^3 \times \rho_{\text{ ice }} \times \text{ g = x} ^3 \times \rho_w \times g \left[ \text{ Volume of the liquid displaced = x}^3 \right]\]

\[ \Rightarrow 0 . 5 \times {10}^3 + x^3 \times (0 . 9) = x^3 \times 1\]

\[ \Rightarrow x^3 \times (0 . 1) = (0 . 5) \times {10}^3 \]

\[ \Rightarrow x^3 = 5 \times {10}^3 \]

\[ \Rightarrow x = 17 . 09 \text{ cm}\]

\[ \Rightarrow x = 17 \text{ cm }\]