For Earth, \(T = 2\pi\sqrt{\frac{1}{g_{earth}}}\)
For Moon, T' = \(2\pi\sqrt{{\frac{1}{g_{moon}}}}\)
Since T = T’
So, \(\frac{l_{moon}}{g_{moon}}=\frac{l_{earth}}{g_{earth}}\) or lmoon = learth (\(\frac{g_{moon}}{g_{earth}}\))= 1 x \(\frac{1}{6}\)
as gmoon = \(\frac{1}{6}g_{earth}\) = \(\frac{1}{6}m\)