Book edition 9th Edition

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

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Let $ρ_{Al}$ represent the density of aluminium and $ρ_{Fe}$ that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius $ρ_{Fe}$ on an equal-arm balance.

The radius of aluminum sphere is $r_{F e} {(\frac{ρ_{F e}}{ρ_{A l}})}^{1 / 3}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identify given data

The density of aluminium is $ρ_{A l}$

The mass of iron is $ρ_{F e}$ .

Step 2: Determine radius of aluminum sphere

The density is the ratio of the mass of an object tothe unit volume of the space. It describes the heavier or lighter among the different objects.

The volume of the aluminum sphere is given by

$V_{A l} = \frac{4}{3} π r_{A l}^{3}$

The volume of the iron sphere is given by

$V_{F e} = \frac{4}{3} π r_{F e}^{3}$

The condition for the equal-arm balanceis given by

$\begin{array}{rcl} m_{a} & = & m_{i} \\ ρ_{A l} V_{A l} & = & ρ_{F e} V_{F e} \end{array}$

Substitute all the values in the above equation.

role="math" localid="1663665328044" $\begin{array}{rcl} ρ_{A l} (\frac{4}{3} π r_{A l}^{3}) & = & ρ_{F e} (\frac{4}{3} π r_{F e}^{3}) \\ r_{A l} & = & r_{F e} {(\frac{ρ_{F e}}{ρ_{A l}})}^{1 / 3} \end{array}$

Therefore, the radius of the aluminum sphere that satisfies the equal-armbalance criterion is $r_{F e} {(\frac{ρ_{F e}}{ρ_{A l}})}^{1 / 3}$ .

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Physics For Scientists & Engineers

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Short Answer

Let $ρ_{Al}$ represent the density of aluminium and $ρ_{Fe}$ that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius $ρ_{Fe}$ on an equal-arm balance.

Step by Step Solution

Step 1: Identify given data

Step 2: Determine radius of aluminum sphere

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Physics For Scientists & Engineers

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Short Answer

Let ρAl represent the density of aluminium and ρFe that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius ρFe on an equal-arm balance.

Step by Step Solution

Step 1: Identify given data

Step 2: Determine radius of aluminum sphere

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Let $ρ_{Al}$ represent the density of aluminium and $ρ_{Fe}$ that of iron. Find the radius of a solid aluminum sphere that balances a solid iron sphere of radius $ρ_{Fe}$ on an equal-arm balance.