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Chapter 1: Problem 9

1.9 If \(P\) is a force and \(x\) a length, what are the dimensions (in the \(F L T \text { system })\) of (a) \(d P / d x\) (b) \(d^{3} P / d x^{3},\) and (c) \(\int P d x ?\)

Short Answer

Expert verified
The dimensions of \(d P / d x\), \(d^{3} P / d x^{3}\), and \(\int P d x\) are \(F/L\), \(F/L^{3}\), and \(FL\) respectively in the FTL system.

Step by step solution

01

Dimension of \(d P / d x\)

The dimension of \(d P / d x\) is obtained by subtracting the dimension of \(x\) (which is L) from the dimension of \(P\) (which is F). This leads to \(F/L\).
02

Dimension of \(d^{3} P / d x^{3}\)

The dimension of \(d^{3} P / d x^{3}\) is obtained by subtracting three times the dimension of \(x\) (which is L) from the dimension of \(P\) (which is F). This results in \(F/L^{3}\).
03

Dimension of \(\int P d x\)

The dimension of \(\int P d x\) is obtained by adding the dimension of \(x\) (which is L) to the dimension of \(P\) (which is F). This gives us \(FL\).

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Most popular questions from this chapter

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