If T=2 π √(l/g), then relative errors in T and l are in the

We have,

$T=2 \pi \sqrt{\frac{l}{g}}$

$\Rightarrow \log T=\log 2 \pi+\frac{1}{2} \log l-\frac{1}{2} \log g$

$\Rightarrow \frac{1}{T} d T=0+\frac{1}{2 l} d l-0 $

$\Rightarrow \frac{d T}{T}=\frac{1}{2} \frac{d l}{l}$

$\Rightarrow \frac{\Delta T}{T}=\frac{1}{2} \frac{\Delta l}{l}$        $[∵ d T \cong \Delta T$ and $d l \cong \Delta l]$

$\Rightarrow \frac{\frac{\Delta T}{T}}{\frac{\Delta l}{l}}=\frac{1}{2}$