Answer
$1 hr, 24 \space min$
Work Step by Step
We know that
$T=\frac{2\pi}{\omega}$
$\implies T=\frac{2\pi}{\sqrt{\frac{g}{R}}}$
We plug in the known values to obtain:
$T=\frac{2\pi}{\sqrt{9.81(6.37\times 10^6)}}$
$T=5060s=1 hr, 24 \space min$
Physics Technology Update (4th Edition)
by Walker, James S.
Published by
Pearson
ISBN 10:
0-32190-308-0
ISBN 13:
978-0-32190-308-2
Chapter 10 - Rotational Kinematics and Energy - Problems and Conceptual Exercises - Page 328: 80
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