Question

The time for one complete cycle, a left swing and a right swing, is called the Period (T), can be found using only the length of the pendulum L, and the force of gravity g.
$T=2\pi \sqrt{\frac{L}{g}}$
This proves that the mass of the pendulum did not affect its period. Based on the equation, which of the following equation could be used to find the length of the pendulum given its period?

• A. $L=\frac{gT}{2\pi }$
• B. $L=\frac{g{T}^2}{4{\pi }^2}$
• C. $L=\frac{T^2}{4{\pi }^{2}g}$
• D. $L=\frac{g}{4{\pi }^2{T}^2}$

Answer 1

Answer: (B)

$L=\frac{g{T}^2}{4{\pi }^2}$

Given equation is $T=2\pi \sqrt{\frac{L}{g}}$

$\Rightarrow T^2=4{\pi }^2\times \frac{L}{g}$

$\Rightarrow T^{2}g=4{\pi }^{2}L$

$\Rightarrow L=\frac{g{T}^2}{4{\pi }^2}$