A student performs an experiment for determination of $g\left(=\frac{4 \pi^{2} \ell}{ T ^{2}}\right), \ell \approx 1 m$, and he commits an error of $\Delta \ell$.
For $T$ he takes the time of $n$ oscillations with the stop watch of least count $\Delta T$ and he commits a human error of $0.1 sec$. For which of the following data, the measurement of $g$ will be most accurate?
(1) $\Delta L =0.5, \Delta T =0.1, n =20$
(2) $\Delta L =0.5, \Delta T =0.1, n =50$
(3) $\Delta L =0.5, \Delta T =0.01, n =20$
(4) $\Delta L =0.1, \Delta T =0.05, n =50$
