Physics 9702 · AS & A Level · Errors and uncertainties

Errors and uncertainties — practice question

The diagram illustrates an experiment for finding the speed of a small ball as it falls through a clear liquid inside a glass tube at constant speed. Two marks are shown on the tube. The upper mark is located at $115 \pm 1\,\text{mm}$ on the nearby rule, while the lower mark is at $385 \pm 1\,\text{mm}$. The ball reaches the upper mark at $1.50 \pm 0.02\,\text{s}$ and reaches the lower mark at $3.50 \pm 0.02\,\text{s}$. The ball's constant speed is found using $\frac{385 - 115}{3.50 - 1.50} = \frac{270}{2.00} = 135\,\text{mm s}^{-1}$. Which expression gives the fractional uncertainty in the speed value?

  • A$\frac{2}{270} + \frac{0.04}{2.00}$
  • B$\frac{2}{270} - \frac{0.04}{2.00}$
  • C$\frac{1}{270} \times \frac{0.02}{2.00}$
  • D$\frac{1}{270} \div \frac{0.02}{2.00}$

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