What is the fractional error in $g$ calculated from $T = 2\pi \sqrt {l/g} $ ? Given fraction errors in $T$ and $l$ are $ \pm x$ and $ \pm y$ respectively?
AIIMS 2012, Easy
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From $T=2 \pi \sqrt{\frac{\ell}{g}} ;$
$g=4 \pi^2 \frac{\ell}{T^2}$
$\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta T}{T}=(y+2 x)$
$g=4 \pi^2 \frac{\ell}{T^2}$
$\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+\frac{2 \Delta T}{T}=(y+2 x)$
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