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The percentage errors in the measurements of the length of a simple pendulum and its time period are 2% and 3% respectively. The maximum error in the value of the acceleration due to gravity obtained from these measurements is

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Detailed Solution

$T = 2 π \sqrt{\frac{l}{g}} or g = 4 π^{2} \frac{1}{T^{2}} or \log g = \log (4 π^{2}) + \log l - 2 \log T .$

The maximum error in g is

$\frac{∆ g}{g} = \frac{∆ l}{l} + 2 \frac{∆ T}{T} = 2 % + 2 \times 3 % = 8 %$

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