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 379: 11a

Answer

$M = m$

Work Step by Step

Since the net gravitational force on the central sphere is zero, the upward force due to the sphere of mass $M$ must be equal in magnitude to the downward force due to the two spheres of mass $m$ Let the distance from the central sphere to the other spheres be $d$ We can find $M$ in terms of $m$: $F = \frac{G~M~m_4}{d^2} = 2 \times\frac{G~m~m_4}{d^2}~sin~30^{\circ}$ $M = 2~m~sin~30^{\circ}$ $M = m$
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