## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 1 - Problems - Page 21: 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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