Question

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

Answer 1

$P_{ice}$ = 0.9 gm/cc

m = 5 kg

Let x $\to$ minimum edge of the ice block in cm.

So, mg = $W_{ice}$ = U

where U = upwards thrust

$\Rightarrow 0.5\times g+x^3\times \rho ice\times g=x^3\times {\rho }_w\times g$

[because, volume of liquid displaced = $x^3$]

$\Rightarrow 0.5\times {10}^3+x^3\times \left(0.9\right)=x^3\times 1$

$\Rightarrow x^3\times \left(0.1\right)=\left(0.5\right)\times {10}^3$

$\Rightarrow x^3=5\times {10}^3$

$\Rightarrow x=17.09$ cm

$x=17cm$.