Question

`T=2\pi √(l/g)`

This is the formula for the period T of a pendulum of length l. Solve this formula for l.

Answer 1

T^2*g / 4pi^2 = l

Explanation:

T = 2 * pi * sqrt( l/g)

We need to solve for l

Divide each side by 2pi

T/ (2pi) = 2 * pi/2pi * sqrt( l/g)

T/ (2pi) = sqrt( l/g)

Now square each side

(T/ (2pi))^2 = ( sqrt( l/g))^2

T^2 / 4pi^2 = l/g

Multiply each side by g

T^2 / 4pi^2 * g= l/g*g

T^2*g / 4pi^2 = l