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,
where l =length of the pendulum and g= acceleration due to gravity on surface of the earth.
Step 2: Find the time period on the surface of the moon.
On the surface of the moon,
Step 3: Find the length of the pendulum on the surface of the moon.
to maintain the second's pendulum time period.
...(ii)
But the acceleration due to gravity at moon is 1/6 of the acceleration due to gravity at earth, i.e.,
Squaring Eq.(iii) and putting this value,