Simple Pendulum

NCERT Class 11, Chapter 2 error analysis applied to $g=\frac{4{\pi }^{2}L}{T^2}$ shows that the fractional error in $g$ is $\frac{\Delta g}{g}=\frac{\Delta L}{L}+2\frac{\Delta T}{T}$, because the period appears squared while the length appears to the first power. The factor of two means any relative error in the period contributes twice as heavily to the error in $g$ as the same relative error in length. Therefore, measuring time carefully, typically by timing many oscillations and dividing, is the most effective way to improve accuracy. The option naming length is wrong because length carries only a first-power dependence and so contributes less than the squared period term. The option about bob mass is wrong because the period of a simple pendulum is independent of mass, so mass does not enter the result. The option about larger amplitude is wrong because large swings violate the small-angle approximation and actually increase error. In practical terms, the timing error per oscillation is reduced by counting many oscillations, since dividing the total time by a large number of swings shrinks the fractional uncertainty in the period proportionally. Because the length contributes only linearly and the period quadratically, an experimenter who has already measured length reasonably well should invest additional effort in precise timing. A consistency check confirms that reducing the doubly weighted period error yields the greatest gain in the precision of g, which is why timing strategy dominates the design of this experiment.