Simple Pendulum

A simple pendulum oscillating through small angles behaves as an SHM system with period $T=2\pi \sqrt{L/g}$, where $L$ is the length and $g$ is the gravitational acceleration. The restoring agent here is the tangential component of gravity, which for small angles is proportional to displacement. Solving for length gives $L=\frac{g{T}^2}{4{\pi }^2}$. Substituting $T=2\text{ s}$ and $g=9.8{\text{ m/s}}^2$, we get $L=\frac{9.8\times 4}{4{\pi }^2}=\frac{39.2}{39.48}\approx 0.99\text{ m}$. The value $0.50\text{ m}$ wrongly uses $T=1\text{ s}$ or halves the result. The value $2.00\text{ m}$ simply copies the period as if it were a length, which is dimensionally invalid. The value $1.96\text{ m}$ omits the $4{\pi }^2$ denominator and instead divides only by 4. This is the classic seconds-pendulum result discussed in NCERT oscillations. As a plausibility check, a seconds pendulum is historically known to be about one metre long, confirming that $0.99\text{ m}$ is the physically expected answer.