College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 1 - Problems: 45

Answer

Since the units for $T^2$ should be $s^2$, we can see that the equation is dimensionally correct.

Work Step by Step

We can analyze the dimensions of the equation $T^2 = \frac{4\pi^2~r^3}{GM}$: $\frac{m^3}{(m^3/kg\cdot s^2)\cdot kg} = \frac{m^3\cdot kg\cdot s^2}{m^3\cdot kg} = s^2$ Since the units for $T^2$ should be $s^2$, we can see that the equation is dimensionally correct.
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