Question

t = 2π√(l/g). this is the formula for the period t of a pendulum of length l. solve this formula for g.

Explanation:

Step1: Square both sides

$T^{2}=(2\pi\sqrt{\frac{l}{g}})^2$
$T^{2}=4\pi^{2}\frac{l}{g}$

Step2: Cross - multiply

$T^{2}g = 4\pi^{2}l$

Step3: Solve for g

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

Answer:

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