For a simple pendulum, time period (T) is given by; T = \(2\pi\sqrt{\frac{l}{g}}\)
At Earth, T = \(2\pi\sqrt{\frac{l}{g}}\) (i)
At Moon, T’=\(v2\pi\sqrt{\frac{l'}{g'}}\) (ii)
Here, T = T’ and g’ = \(\frac{1}{6}g\)
So, from equation (i) & (ii)
\(\frac {l}{g}=\frac{l'}{g'}\)
or,\(l'=\frac{g'}{g}\times l\)
= \(\frac{1}{6}g\times\frac{1}{g}\times l\)
= \(\frac{1}{6}\times l\)
= \(\frac{1}{6}\)× 100 cm
= 16.7 cm