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

3/4 filled with water

Step-by-step 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=(1)/(4)V* \rho_wg`

As all the forces are conserved

`W_b+xV\rho_wg=V\rho_wg\\\Rightarrow (1)/(4)V* \rho_wg+xV\rho_wg=V\rho_wg\\\Rightarrow (1)/(4)+x=1\\\Rightarrow x=1-(1)/(4)\\\Rightarrow x=(2)/(3)`

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