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 = 5 kg
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
$$\begin{gathered} \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ 0.5\times g+x^3\times {\rho }_{ice}\times g=x^3\times {\rho }_w\times g\left[\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{liquid}\mathrm{displaced}=x^3\right] \\ \Rightarrow 0.5\times {10}^3+x^3\times (0.9)=x^3\times 1 \\ \Rightarrow x^3\times (0.1)=(0.5)\times {10}^3 \\ \Rightarrow x^3=5\times {10}^3 \\ \Rightarrow x=17.09\mathrm{cm} \\ \Rightarrow x=17\mathrm{cm} \end{gathered}$$