Question

A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water ? Density of iron = 8000 kg $m^{-3}$ and density of water = 1000 kg $m^{-3}$.

Answer 1

Let X $\to$ external edge

${\rho }_1=8000kg/m^3$

= 8 gm/u

${\rho }_w=1000kg/m^3$

= 1gm/u

$\therefore$ w=u

For the given condition,
Weight of the box = Buoyant force

$\Rightarrow V_{1}g=v{\rho }_{w}g$

$\Rightarrow (x^2\times (0.1)\times 6)\times 8=x^3\times 1$
[Because, volume of iron = $v_1$ = 6 volume of each sheet]

$\Rightarrow$ x = 4.8 cm