### Select your language

Suggested languages for you:

Americas

Europe

Q52PE

Expert-verified
Found in: Page 397

### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

### Answers without the blur.

Just sign up for free and you're in.

# Referring to Figure $11.21$ , prove that the buoyant force on the cylinder is equal to the weight of the fluid displaced (Archimedes’ principle). You may assume that the buoyant force is ${F}_{2}-{F}_{1}$ and that the ends of the cylinder have equal areas A. Note that the volume of the cylinder (and that of the fluid it displaces) equals $\left({h}_{2}-{h}_{1}\right)A$ .

The buoyant force acting on the body is equal to the weight of the object which is submerged into the liquid.

See the step by step solution

## Step 1: Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

## Step 2: Given data

The ratio of the object's density to the density of the fluid in which it is immersed determines the fraction submerged in the fluid.

Sketch of the figure

## Step 3: Derivation of the formula of buoyant force

Here the ${F}_{by}$ = buoyant force acting on the body

The two surfaces are named as A and B there the force is acted.

${F}_{by}={F}_{b}-{F}_{T}$

${F}_{by}={F}_{b}-{F}_{T}\phantom{\rule{0ex}{0ex}}={P}_{b}{A}_{b}-{P}_{T}{A}_{T}\phantom{\rule{0ex}{0ex}}=\left({h}_{2}{\rho }_{w}g\right)A-\left({h}_{1}{\rho }_{w}g\right)A\phantom{\rule{0ex}{0ex}}={\rho }_{w}×g×A\left[{h}_{2}-{h}_{1}\right]$

Further simplifying, we get

${F}_{by}={\rho }_{w}×g×{V}_{wd}\phantom{\rule{0ex}{0ex}}={m}_{wd}g\phantom{\rule{0ex}{0ex}}={W}_{wd}$

Hence, the buoyant force acting on the body is equal to the weight of the object which is submerged into the liquid.

### Want to see more solutions like these?

Sign up for free to discover our expert answers

## Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.