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Question

If the error in measuring the time period of a simple pendulum is 1% and error in measuring the amplitude is 1%, then maximum possible error in measuring the maximum acceleration of the bob is

Moderate

Solution

Maximum accelaration $a = ω^{2} A = \frac{4 π^{2} . A}{T^{2}} = 4 π^{2} . {AT}^{- 2}$
$∴ {(\frac{∆ a}{a})}_{\max} x 100 % = \frac{∆ A}{A} x 100 % + 2 (\frac{∆ T}{T}) x 100 % = 1 % + 2 x 1 % = 3 %$

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