## Length of Pendulum Increading by Factor of 9 Increaeses Period By 1 Second - Find Length and Period

If the length of a simple pendulum increases by a factor of 9, the period increases from\[t\]

to \[t+1\]

. What is \[T\]

and what is the length of the pendulum?The period of a pendulum is given by

\[T= 2 \pi \sqrt{ \frac{l}{g}}\]

.Originally

\[t= 2 \pi \sqrt{ \frac{L}{g}}\]

, and then \[t+1= 2 \pi \sqrt{ \frac{9L}{g}}\]

.Dividing the second equation by the first gives

\[\frac{t+1}{t}= \sqrt{9}=3\]

.Then

\[t+1=3t \rightarrow 1=2t \rightarrow t=0.5\]

.Then

\[T= 2 \pi \sqrt{\frac{l}{g}} \rightarrow l = \frac{gT^2}{4 \pi^2} =\frac{9.8 \times 0.5^2}{39.47}=0.062\]

m to 3 decimal places.