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  4. What is the fractional error in g calculated from T=2π√(l/g) if it is given that fractional errors in T and l are ± x and ± y, respectively?

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Q. What is the fractional error in $g$ calculated from $T=2\pi\sqrt{\frac{l}{g}}$ if it is given that fractional errors in $T$ and $l$ are $\pm x$ and $\pm y$, respectively?

Physical World, Units and Measurements

Solution:

$g=\frac{4\pi^{2}l}{T^{2}}$
$\Rightarrow \frac{\Delta g}{g}=\frac{\Delta l}{l}+2\frac{\Delta T}{T}$
$\Rightarrow \frac{ \Delta g}{g}=y+2x$