Can dimensional analysis determine whether the area of a circle is πr2 or 2πr2? Explain.
Answer to Problem 1CQ
Explanation of Solution
Write the dimensional formula for the area of the circle
Here,
Write the dimensional formula for the area of the circle
Here,
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
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
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