Select your language

Suggested languages for you:
Log In Start studying!
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q.73

Expert-verified
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 387

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

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 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.

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.