Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P14.36. The bulb of a syringe is squeezed and released to let the atmosphere lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. The rod, of length $L$ and average density $ρ_{0}$ , floats partially immersed in the liquid of density $ρ$ . A length $h$ of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by role="math" localid="1663764227560" $ρ = \frac{ρ_{0} L}{L - h}$ .

It is proved that the density of the liquid is $ρ = \frac{ρ_{0} L}{L - h}$ .

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TABLE OF CONTENTS :

TABLE OF CONTENTS

Given data:

The length of the rod is $L$ .

The length of the rod not immersed in the liquid is $h$ .

The average density of the rod is $ρ_{0}$ .

The density of the liquid is $ρ$ .

Buoyancy and gravitational force:

The buoyant force from a liquid of density $d$ when volume of the liquid displaced $v$ is,

$B = g d v$ ….. (1)

Here, $g$ is the acceleration due to gravity.

The gravitational force on a body of mass $m$ is,

$F = m g$ ….. (2)

Show that the density of the liquid is ρ=ρ0LL−h:

Length of the rod immersed in the liquid is $L - h$ .

Let $A$ be the cross sectional area of the rod. Volume of the rod immersed in the liquid is $A (L - h)$ .

This is also the volume of the liquid displaced. From equation (1), the buoyancy force on the rod directed upward is,

$B = ρ g A (L - h)$

The total volume of the rod is $A L$ and thus its mass is $ρ_{0} A L$ . Thus from equation (2), the gravitational force acting on the rod directed downward is,

$F = ρ_{0} A L g$

At equilibrium, these two forces cancel each other. Thus

$ρ g A (L - h) = ρ_{0} A L g ρ = \frac{ρ_{0} L}{L - h}$

Hence it is proved.

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Short Answer

Step by Step Solution

Given data:

Buoyancy and gravitational force:

Show that the density of the liquid is ρ=ρ0LL−h:

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Given data:

Buoyancy and gravitational force:

Show that the density of the liquid is ρ=ρ0LL−h:

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