Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A neutron star is a stellar object whose density is about that of nuclear matter, $2 \times 10^{17} kg / m^{3}$ . Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?

The value of the radius of the star is 13 km.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The density of the nuclear matter, $p = 2 \times 10^{17} kg / m^{3}$

Mean density of Sun according to Appendix C, $p_{s} = 1410 \times 10^{17} kg / m^{3}$

Mean radius of Sun according to Appendix C, $R_{s} = 6.96 \times 10^{8} m$

Step 2: Understanding the concept of density

As per the given concept, the Sun is to collapse to form into a star whose density is given. Thus, keeping the mass constant and relating this to the density, volume, and mass relation, we can get that the radius' cube value is inversely proportional to the density. Thus, using this proportionality relation, we can get the required value.

Formula:

The density of a spherical object, $p = \frac{m}{\frac{4}{3} π R^{3}} . . . . . . . (1)$

Step 3: Calculation of the radius of the star

From equation (1), we get that

$p α \frac{1}{R^{3}}$ with all other terms as costant.

$R α \frac{1}{p^{1 / 3}}$

Thus, using this above relation and the given data, we can get the radius of the star as follows:

$R = R_{s} {[\frac{p_{s}}{p}]}^{1 / 3} = (6.96 \times 10^{8} m) {[\frac{(1410 \times 10^{17} kg / m^{3})}{(2 \times 10^{17} kg / m^{3})}]}^{1 / 3} = 1.3 \times 10^{4} m = 13 km$

Hence, the value of the radius is 13 km.

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Fundamentals Of Physics

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Short Answer

A neutron star is a stellar object whose density is about that of nuclear matter, $2 \times 10^{17} kg / m^{3}$ . Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?

Step by Step Solution

Step 1: Given data

Step 2: Understanding the concept of density

Step 3: Calculation of the radius of the star

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Step by Step Solution

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A neutron star is a stellar object whose density is about that of nuclear matter, $2 \times 10^{17} kg / m^{3}$ . Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?