Question
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?
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Answer
From $T = 2\pi \sqrt {\frac{\ell }{g};} \,g = 4{\pi ^2}\frac{\ell }{{{T^2}}}$
$\frac{{\Delta g}}{g} = \frac{{\Delta \ell }}{\ell } + \frac{{2\Delta T}}{T} = \left( {y + 2x} \right)$
$\frac{{\Delta g}}{g} = \frac{{\Delta \ell }}{\ell } + \frac{{2\Delta T}}{T} = \left( {y + 2x} \right)$
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