First slide

Accuracy; precision of instruments and errors in measurements

Question

Calculate percentage error in determination a time period of a pendulum
$T =2 π \sqrt{\frac{l}{g}} or 2 π {(\frac{l}{g})}^{1 / 2}$ where, l and g are measured with ± 2% and ± 3% errors.

Moderate

A

2.9%
B

± 2.5%
C

1.5%
D

± 1.9%

Solution

$\begin{array}{l} \frac{ΔT}{T} \times 100 = \pm (\frac{1}{2} \times \frac{Δl}{l} \times 100 + \frac{1}{2} \times \frac{Δg}{g} \times 100) \\ = \pm (\frac{1}{2} \times 2 + \frac{1}{2} \times 3) = \pm 2 .5 % \end{array}$

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