Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 1 - Introduction to Physics - Conceptual Questions - Page 14: 1

Answer

No, It is not possible to determine whether the area of the circle is $\pi r ^{2}$ or 2 $\pi r ^{2}$

Work Step by Step

We know that the dimension of both $\pi r^2$ and $2\pi r^2$ is $L^2$. The factor $2$ is a dimensionless constant and therefore dimensional analysis cannot determine whether the area of a circle is $\pi r^2$ or $2\pi r^2$.
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