The length of a second's pendulum on the surface of earth is 1 m. What will be the length of a second's pendulum on the moon?

Hint: The time period remains the same.
Step 1: Find the time period on the surface of the earth.
A second's pendulum means a simple pendulum having a time period, T=2 s
For a simple pendulum,         T=2πlg
where l =length of the pendulum and g= acceleration due to gravity on surface of the earth.
                                            Te=2πlege                                             ...(i)
Step 2: Find the time period on the surface of the moon.
On the surface of the moon,        Tm=2πlmgm
Step 3: Find the length of the pendulum on the surface of the moon.
                                               TeTm=2π2πlege×gmlm
Te=Tm to maintain the second's pendulum time period.
                                                 1=lelm×gmge                              ...(ii)
But the acceleration due to gravity at moon is 1/6 of the acceleration due to gravity at earth, i.e.,                              gm=ge6
Squaring Eq.(iii) and putting this value,
                                                      1=lelm×ge/6ge=lelm×16
                                            le6lm=16lm=le
                                             lm=16le=16×1=16m