Physics - Error Question with Solution | TestHub

$\mathrm{T}=2\pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}}};\log \mathrm{T}=\log (2\pi )+\frac{1}{2}\log \left(\frac{\mathrm{l}}{\mathrm{g}}\right)\Rightarrow \log \mathrm{T}=\log (2\pi )+\frac{1}{2}\log (1)-\frac{1}{2}\log (\mathrm{g})$ Differentiating $\frac{\Delta \mathrm{T}}{\mathrm{T}}=0+\frac{1}{2}\times \frac{\Delta \mathrm{l}}{\mathrm{l}}-0\Rightarrow \frac{\Delta \mathrm{T}}{\mathrm{T}}\times 100=\frac{1}{2}\times \frac{\Delta \mathrm{l}}{\mathrm{l}}\times 100$ $=\frac{1}{2}\times 21=10.5\approx 10\%$ Note: In this method, the $\%$ error obtained is an approximate value on the higher side. Exact value is less than the obtained one.