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Q.73

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Found in: Page 387

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# In , a cone of density and total height floats in a liquid of density . The height of the cone above the liquid is . What is the ratio of the exposed height to the total height?

The ratio of is .

See the step by step solution

## Step 1: Definition for Archimedes' principle

According to Archimedes' principle, a body immersed in a fluid is subjected to an upwards force equal to the weight of the displaced fluid. This is the initial state of equilibrium. The force of buoyancy, also known as the buoyancy force, is assumed to be located in the middle of the submerged hull, also known as the center of buoyancy.

## Step 2: Introduction

The Archimedes principle determines the buoyant force on the cone.

The cone's gravitational force will be equal to the cone's gravitational force.

At the center of gravity, the gravitational force will act.

## Step 3: Calculation of

The volume of a cone is expressed as:

Where, is the proportionality constant and is the height of the cone. The buoyant force is expressed as follows:

Where. is the density of fluid, is the proportionality constant, is the height of cone, is the height above the water and is the acceleration due to gravity.

The expession for gravitational force is given as:

Where, is the density of cone, is the proportionality constant, / is the height of cone and is the acceleration due to gravity.

As a result, the gravitational and buoyant forces are identical.