The correct answer is C because:

Find the average value of diameter, d:
- Average d = $\frac{0.32 + 0.34 + 0.33 + 0.32 + 0.31}{5}$ = 0.324 mm
Find the absolute uncertainty in d:
- Absolute uncertainty in d = $\frac{1}{2}$ (range) = $\frac{1}{2}$ (0.34 - 0.31) = 0.015 mm
Find the percentage uncertainty in diameter, d:
- Percentage uncertainty = $\frac{a b s o l u t e u n c e r t a i n t y}{v a l u e} \times 100 %$
- Percentage uncertainty in d = $\frac{0.015}{0.324} \times 100 %$ = 4.63%
Find the percentage uncertainty in the cross-sectional area, A:
- Since cross-sectional area, $A = π \times {(\frac{d}{2})}^{2} = \frac{π}{4} d^{2}$ the percentage uncertainty in d must be doubled.
- 4.63 % x 2 = 9.26%

A is incorrect as the answer is half of the correct value. This would be the result of incorrectly halving the percentage uncertainty before doubling it, or just not doubling it.

B is incorrect as the percentage uncertainty has been halved and squared, as opposed to doubled.

D is incorrect as the answer is twice the value it should be. This would be the result of not halving the range when finding the absolute uncertainty.

Remember:
- The percentage uncertainty in a range of results is $\frac{\frac{1}{2} (r a n g e)}{m e a n} \times 100 %$ .
- When raising a quantity to a power you should multiply the percentage uncertainty by that power.
Since $A = \frac{π}{4} d^{2}$ , the percentage uncertainty in d only needs to be doubled due d being squared. The $\frac{π}{4}$ , being a constant, has no percentage uncertainty so will not add to the percentage uncertainty in A.

Quantity	Percentage uncertainty
F	5.3
ε	1.2
d	1.0

Measurements & Uncertainties (OCR AS Physics)

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