Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

In Problem 1, What ratio m / M gives the least gravitational potential energy for the system?

Ratio $\frac{m}{M}$ which gives least gravitational potential energy is 0.5

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

Mass of particle is M
Mass of another particle is M - m

Step 2: Understanding the concept of the energy

To find the ratio, use the formula for gravitational potential energy in which potential energy is proportional to the product of masses and inversely proportional to the distance between the masses.

Formula:

Potential Energy, $U = - \frac{G M m}{r}$ (i)

Step 3: Calculation of ratio which gives least potential energy

Ratio of m / M which gives minimum potential energy using equation (i):

$U = - \frac{G m (M - m)}{r}$

To find minimum potential energy,

$\frac{d U}{d m} = 0 - \frac{G (M - 2 m)}{r} = 0 M - 2 m = 0 M = 0.5 m \frac{m}{M} = 0.5$

Hence, the ratio at which we obtain least potential energy is 0.5

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Fundamentals Of Physics

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Short Answer

In Problem 1, What ratio m / M gives the least gravitational potential energy for the system?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of the energy

Step 3: Calculation of ratio which gives least potential energy

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Fundamentals Of Physics

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Short Answer

In Problem 1, What ratio m / M gives the least gravitational potential energy for the system?

Step by Step Solution

Step 1: The given data

Step 2: Understanding the concept of the energy

Step 3: Calculation of ratio which gives least potential energy

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