Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 13 - Gravitation - Problems - Page 380: 19

Answer

$2.65 ×10^6m$

Work Step by Step

Let 'd' be the altitude and 'm' be the mass of the body. From Newton's law of universal gravitation $F=\frac{GM_Em}{r^2}$ but $F=ma$ so $ma=\frac{GM_Em}{r^2}$ $a=\frac{GM_E}{r^2}$ $r=\sqrt\frac{GM_E}{a}$ putting the we values, we get $r=\sqrt\frac{6.67\times10^{-11}\times5.98\times10^{24}}{4.9}=9.02\times10^6m$ now we can find $'d'$that is altitude, it is the difference between$'r'$ and radius of earth $'r_E'$ $d=r-r_E$ putting the values we get $d=9.02\times10^6-6.37\times10^6$ $d=2.65\times10^6m$
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