Question

The rectangular boat shown below has base dimensions 10.0 cm × 8.0 cm. Each cube has a mass of 40 g, and the liquid in the tank has a density of 1.0 g/mL. How far has the boat sunk into the water?

Answer 1

When boat is sunk into the liquid the net buoyancy on the boat is counterbalanced by weight of the boat

So here weight of the boat = Buoyancy force

let say boat is sunk by distance "h"

now we can say

$F_b = \rho * V * g$

$F_b = 1000*0.10 * 0.08 * h * 9.8$

now by above force balance equation we can write

$m*g = F_b$

$0.040 * 9.8 = 1000 * 0.10 * 0.08 * h * 9.8$

$0.040 = 8h$

$h = 5 * 10^{-3} m$

so boat will sunk by total 5 mm distance