College Physics, Volume 1
College Physics, Volume 1
2nd Edition
ISBN: 9781133710271
Author: Giordano
Publisher: Cengage
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Chapter 1, Problem 1Q

Suppose a friend told you that the density of a sphere is 4 3 π r 4 , where r is the radius of the sphere. Compute the dimensions of this expression and show that it cannot be correct.

Expert Solution & Answer
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To determine

The dimension of the expression and evaluate.

Answer to Problem 1Q

The expression (4/3)πr4 cannot be the equation for density.

Explanation of Solution

In the expression (4/3)πr4, only radius, r has dimension and all others are dimensionless quantity. The radius is a dimension of length.  Hence, the expression (4/3)πr4 will have a dimension L4.

Write the equation for density of the sphere.

    density=massvolume        (I)

Hence, from equation (I), the dimension of density is M/L3.

 Conclusion:

Since both the expression has different dimensions, (4/3)πr4 cannot be the equation for density.

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