In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\)

\(\begin{array}{l}
T = \frac{{30\,\sec }}{{20}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta T = \frac{1}{{20}}\sec ,\\
\,\,\,\,\,\,\,L = 55\,cm\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta L = 1\,mm = 0.1\,cm\\
\,\,\,\,\,\,\,g = \frac{{4{\pi ^2}L}}{{{T^2}}}\\
\,\,\,\,\,\,\,\,percentage\,error\,in\,g\,is\\
\,\,\,\,\,\,\,\,\,\frac{{\Delta g}}{g} \times 100 = \left( {\frac{{\Delta L}}{L} + \frac{{2\Delta T}}{T}} \right)100\% \\
\,\,\,\,\,\,\,\,\,\,\, = \left( {\frac{{0.1}}{{5.5}} + 2\frac{{\left( {\frac{1}{{20}}} \right)}}{{\frac{{30}}{{20}}}}} \right)100\%  \simeq 6.8\% .
\end{array}\)