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Chapter 1: Problem 120

If the length of rod \(\mathrm{A}\) is \((2.35 \pm 0.01) \mathrm{cm}\) and that of \(\mathrm{B}\) is \((5.68 \pm 0.01) \mathrm{cm}\) then the rod \(\mathrm{B}\) is longer than \(\mathrm{rod} \mathrm{A}\) by \(\ldots\) (a) \((2.43 \pm 0.00) \mathrm{cm}\) (b) \((3.33 \pm 0.02) \mathrm{cm}\) (c) \((2.43 \pm 0.01) \mathrm{cm}\) (d) \((2.43 \pm 0.001) \mathrm{cm}\)

Short Answer

Expert verified
(b) \( (3.33 \pm 0.02) \mathrm{cm}\)

Step by step solution

01

Identify the length of each rod with its uncertainty

We have the following information: Length of rod A: \(2.35 \pm 0.01 \mathrm{cm}\) Length of rod B: \(5.68 \pm 0.01 \mathrm{cm}\)
02

Calculate the difference in length between rod B and rod A

Subtract the length of rod A from the length of rod B to get the difference: Difference = Length of rod B - Length of rod A = \(5.68 \mathrm{cm} - 2.35 \mathrm{cm} = 3.33 \mathrm{cm}\)
03

Calculate the uncertainty in the difference

To find the uncertainty in the difference, we will add the uncertainties of each individual measurement: Uncertainty of the difference = Uncertainty of rod A + Uncertainty of rod B = \(0.01\mathrm{cm} + 0.01\mathrm{cm} = 0.02\mathrm{cm}\)
04

Write the final answer with uncertainty

The length difference between rod B and rod A is: \(3.33 \pm 0.02 \mathrm{cm}\) Answer: (b) \( (3.33 \pm 0.02) \mathrm{cm}\)

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