Physics - Error Question with Solution | TestHub

$\therefore T=2\pi \sqrt{\frac{l}{g}}\Rightarrow g=4{\pi }^2\frac{l}{T^2}$

$\therefore$Error in$g$can be calculated as

$\frac{\mathrm{\Delta }g}{g}=\frac{\mathrm{\Delta }\mathrm{l}}{l}+\frac{2\mathrm{\Delta }\mathrm{T}}{T}$.

$\therefore$Total time for$n$oscillation is$t=nT$where$T$= time for oscillation.

$\Rightarrow \frac{\mathrm{\Delta }\mathrm{t}}{t}=\frac{\mathrm{\Delta }T}{T}$

$\Rightarrow \frac{\mathrm{\Delta }g}{g}=\frac{\mathrm{\Delta }l}{l}+\frac{2\mathrm{\Delta }\mathrm{t}}{t}$

Given that$\mathrm{\Delta }l=1 \mathrm{mm}={10}^{-3} \mathrm{m}, l=20\times {10}^{-2} \mathrm{m}$

$\mathrm{\Delta }t=1 \mathrm{s},\mathrm{ t}=90 \mathrm{s}$.

$\mathrm{\%}\mathrm{ }\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\mathrm{ }\mathrm{i}\mathrm{n}\mathrm{ }g is$

$\frac{\mathrm{\Delta }g}{g}\times 100=\left(\frac{\mathrm{\Delta }l}{l}+\frac{2\mathrm{\Delta }t}{t}\right)\times 100$

$=\left(\frac{{10}^{-3}}{20\times {10}^{-2}}+\frac{2\times 1}{90}\right)\times 100$$=\frac{1}{2}+\frac{20}{9}$$=0.5+2.22$$=2.72\mathrm{\%}$

$\cong 3\mathrm{\%}$