Kevin S. Huang

2016: Problem 25

Topic: Other
Concepts: Error propagation

Solution:

Recall independent errors add in quadrature:

\Delta(A+B)=\sqrt{(\Delta A)^2+(\Delta B)^2}

Alice: One measurement with uncertainty $\Delta L_2=2\,\mathrm{mm}$ .

\Delta L_{\text{Alice}}=\Delta L_2=2\,\mathrm{mm}

Bob: Two measurements with uncertainty $\Delta L_2=2\,\mathrm{mm}$ added together.

\Delta L_{\text{Bob}}=\sqrt{(\Delta L_2)^2+(\Delta L_2)^2}=\sqrt{2}(\Delta L_2)=2.8\,\mathrm{mm}

Christina: Two measurements with uncertainty $\Delta L_1=1\,\mathrm{mm}$ added together.

\Delta L_{\text{Christina}}=\sqrt{(\Delta L_1)^2+(\Delta L_1)^2}=\sqrt{2}(\Delta L_1)=1.4\,\mathrm{mm}

Thus,

\Delta L_{\text{Christina}}<\Delta L_{\text{Alice}}<\Delta L_{\text{Bob}}

so the answer is A.