Understanding Wooden Cube Floating in Water

When a wooden cube floats in water, it means that the upward buoyant force exerted by the water on the submerged part of the cube is equal to the downward weight of the entire wooden cube. This principle is known as Archimedes' Principle.

Key Principles of Floating Objects

• For an object to float, its average density must be less than or equal to the density of the fluid it is in.
• When an object floats, the weight of the object is equal to the weight of the fluid displaced by its submerged portion.
• The volume of fluid displaced is equal to the volume of the submerged part of the object.

Given Information

Let's list the information provided in the question:

• Side of the wooden cube (\(s\)) = 0.2 m
• Density of wood (\(\rho_{wood}\)) = 600 kg/m\(^3\)
• The cube is floating in water.

Required Information (Standard Values)

To solve this problem, we also need the standard density of water:

• Density of water (\(\rho_{water}\)) = 1000 kg/m\(^3\)

Calculating Wooden Cube Volume

First, we need to find the total volume of the wooden cube.

The volume of a cube is given by the formula:

\[ V_{cube} = s^3 \]

Substitute the given side length:

\[ V_{cube} = (0.2 \text{ m})^3 \]

\[ V_{cube} = 0.008 \text{ m}^3 \]

Applying Archimedes' Principle for Floating

According to Archimedes' Principle for a floating object:

Weight of the wooden cube = Weight of the water displaced

We know that weight (\(W\)) = mass (\(m\)) \(\times\) acceleration due to gravity (\(g\)).

Also, mass (\(m\)) = density (\(\rho\)) \(\times\) volume (\(V\)).

So, we can write the equation as:

\[ \rho_{wood} \times V_{cube} \times g = \rho_{water} \times V_{displaced} \times g \]

Since \(g\) is on both sides, it cancels out:

\[ \rho_{wood} \times V_{cube} = \rho_{water} \times V_{displaced} \]

We want to find the volume of water displaced (\(V_{displaced}\)). Rearrange the formula:

\[ V_{displaced} = \frac{\rho_{wood} \times V_{cube}}{\rho_{water}} \]

Substituting Values and Calculating Volume Displaced

Now, let's substitute the known values into the equation:

• \(\rho_{wood}\) = 600 kg/m\(^3\)
• \(V_{cube}\) = 0.008 m\(^3\)
• \(\rho_{water}\) = 1000 kg/m\(^3\)

\[ V_{displaced} = \frac{600 \text{ kg/m}^3 \times 0.008 \text{ m}^3}{1000 \text{ kg/m}^3} \]

\[ V_{displaced} = \frac{4.8}{1000} \text{ m}^3 \]

\[ V_{displaced} = 0.0048 \text{ m}^3 \]

Converting Volume to Liters

The options are given in Liters (Ltr). We know that:

1 m\(^3\) = 1000 Ltr

So, to convert 0.0048 m\(^3\) to Liters:

\[ V_{displaced} = 0.0048 \text{ m}^3 \times 1000 \text{ Ltr/m}^3 \]

\[ V_{displaced} = 4.8 \text{ Ltr} \]

Summary Table of Calculations

Thus, the volume of water displaced by the wooden block is 4.8 Liters.