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Q. If the percentage error in length is 0.1% and in time is 0.4% then % error in g will be

JIPMERJIPMER 2016Physical World, Units and Measurements

Solution:

$T = 2\pi \sqrt{\frac{l}{g}} or g = \frac{4\pi^{2}l}{T^{2}}$
Then, % error in g
$= \left(\frac{\Delta l}{l}\times100\right)+2\left(\frac{\Delta T}{T }\times100\right)$
$ = 0.1\% + 2(0.4) \% = 0.9\%$