First slide

Accuracy; precision of instruments and errors in measurements

Question

Calculate percentage error in determination a time period of a pendulum
$T = 2 π \sqrt{\frac{l}{g}} o r 2 π {(\frac{l}{g})}^{1 / 2}$
where, l and g are measured with $\pm 2 % a n d \pm 3 % e r r o r s .$

Moderate

A

2.9%
B

$\pm 2.5 %$
C

1.5%
D

$\pm 1.9 %$

Solution

$\frac{Δ T}{T} \times 100 = \pm (\frac{1}{2} \times \frac{Δ l}{l} \times 100 + \frac{1}{2} \times \frac{Δ g}{g} \times 100)$
$= \pm (\frac{1}{2} \times 2 + \frac{1}{2} \times 3) = \pm 2.5 %$

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