Question

A cube of each side L floats in a liquid of density 3 times the
density of cube. What length of cube will be outside the
liquid ?​

Answer 1

Answer:

I also don't know the answer

Answer 2

Given:

The edge length of the cube = L

The density of the liquid = 3 X The density of the cube

To find:

The length of the cube that will be outside the liquid

Solution:

The Archimedes Principle states that  the buoyant force acting on an object equals the weight of the liquid displaced by the object.

or Fb = V X ρ X g

⇒ V ∝ 1 / ρ     - (1)

where V is the volume of the liquid displaced and ρ is the density of the liquid.

Let y be the length of the cube that is inside the liquid.

⇒ The volume of the immersed part of the liquid = y X L X L

The total volume of the cube = L³

From equation 1,

V is inversely proportional to the density

⇒ $\frac{yL^2}{L^3} = \frac{1}{3}$

or 3y = L

or y = L / 3

The length of the cube outside the liquid = L - Y = L - L/3

= 2L/3

Hence, $\frac{2L}{3}$  length of the cube will be outside the  liquid.