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If the length of a simple pendulum increases from  
\[L\]
  to  
\[L+0.1\]
  the period doubles. Find  
\[L\]
.
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  
\[2T= 2 \pi \sqrt{ \frac{L+0.1}{g}}\]
.
Dividing the second equation by the first gives  
\[2= \sqrt{ \frac{L+0.1}{L}}\]
.
Then  
\[4= \frac{L+0.1}{L} \rightarrow 4L=L+0.1 \rightarrow 3L=0.1 \rightarrow L=\frac{0.1}{3}= \frac{1}{30}\]
m.