Question

A hollow cubical box is 0.221 m on an edge. This box is floating in a lake with 1/4 of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink

Answer 1

Answer:

3/4 filled with water

Explanation:

x = Fraction of box filled

g = Acceleration due to gravity = 9.81 m/s²

$\rho_w$ = Density of water

V = Volume of water

Weight of empty box is equal to the weight of the water displaced

$W_b=\frac{1}{4}V\times \rho_wg$

As all the forces are conserved

$W_b+xV\rho_wg=V\rho_wg\\\Rightarrow \frac{1}{4}V\times \rho_wg+xV\rho_wg=V\rho_wg\\\Rightarrow \frac{1}{4}+x=1\\\Rightarrow x=1-\frac{1}{4}\\\Rightarrow x=\frac{2}{3}$

So, the box starts to sink when the box is 3/4 filled with water