Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 13 - Newton's Theory of Gravity - Exercises and Problems: 3

Answer

(a) The gravitational force that each ball exerts on the other is $6.67\times 10^{-9}~N$ (b) The ratio of this gravitational force to the weight of the 100-gram ball is $6.81\times 10^{-9}$

Work Step by Step

(a) We can find the magnitude of the gravitational force of attraction that each ball exerts on the other. $F = \frac{G~M_1~M_2}{R^2}$ $F = \frac{(6.67\times 10^{-11}~m^3/kg~s^2)(10~kg)(0.10~kg)}{(0.10~m)^2}$ $F = 6.67\times 10^{-9}~N$ The magnitude of the gravitational force of attraction that each ball exerts on the other is $6.67\times 10^{-9}~N$. (b) We can find the ratio of this gravitational force to the weight of the 100-gram ball. $\frac{F}{M_2~g} = \frac{6.67\times 10^{-9}~N}{(0.10~kg)(9.80~m/s^2)} = 6.81\times 10^{-9}$ The ratio of this gravitational force to the weight of the 100-gram ball is $6.81\times 10^{-9}$.
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