Physics (5th Edition)
Physics (5th Edition)
5th Edition
ISBN: 9780321976444
Author: James S. Walker
Publisher: PEARSON
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Textbook Question
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Chapter 1, Problem 1CQ

Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain.

Expert Solution & Answer
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To determine
Whether the dimensional analysis determine the area of circle is πr2 or 2πr2 .

Answer to Problem 1CQ

The dimensional analysis cannot determine whether the area of a circle is πr2 or 2πr2 .

Explanation of Solution

Write the dimensional formula for the area of the circle πr2 .

πr2=[L0][L2]=[L2] (1)

Here,

L is the dimension of the length.

Write the dimensional formula for the area of the circle 2πr2 .

2πr2=[L0][L0][L2]=[L2] (2)

Here,

L is the dimension of the length.

From the equation (1) and (2) the dimension of the area is same in both cases. So that the dimensional analysis cannot be determine whether the area of a circle is πr2 or 2πr2 .

The dimensions of the variable do not depend on the numeric number.

Conclusion:

Therefore, the dimensional analysis cannot determine whether the area of a circle is πr2 or 2πr2 .

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